# Haversine formula

Haversine formula
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The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.

It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical "triangles".

Implement a great-circle distance function, or use a library function, to show the great-circle distance between:

• Nashville International Airport (BNA)   in Nashville, TN, USA,   which is:
```   N 36°7.2',   W 86°40.2'     (36.12,   -86.67)           -and-
```
• Los Angeles International Airport (LAX)  in Los Angeles, CA, USA,   which is:
```   N 33°56.4',  W 118°24.0'    (33.94,  -118.40)
```

```User Kaimbridge clarified on the Talk page:

-- 6371.0 km is the authalic radius based on/extracted from surface area;
-- 6372.8 km is an approximation of the radius of the average circumference
(i.e., the average great-elliptic or great-circle radius), where the
boundaries are the meridian (6367.45 km) and the equator (6378.14 km).

Using either of these values results, of course, in differing distances:

6371.0 km -> 2886.44444283798329974715782394574671655 km;
6372.8 km -> 2887.25995060711033944886005029688505340 km;
(results extended for accuracy check:  Given that the radii are only
approximations anyways, .01' ≈ 1.0621333 km and .001" ≈ .00177 km,
practical precision required is certainly no greater than about
.0000001——i.e., .1 mm!)

As distances are segments of great circles/circumferences, it is
recommended that the latter value (r = 6372.8 km) be used (which
```

Most of the examples below adopted Kaimbridge's recommended value of 6372.8 km for the earth radius. However, the derivation of this ellipsoidal quadratic mean radius is wrong (the averaging over azimuth is biased). When applying these examples in real applications, it is better to use the mean earth radius, 6371 km. This value is recommended by the International Union of Geodesy and Geophysics and it minimizes the RMS relative error between the great circle and geodesic distance.

## ABAP

`   DATA: X1 TYPE F, Y1 TYPE F,        X2 TYPE F, Y2 TYPE F, YD TYPE F,        PI TYPE F,        PI_180 TYPE F,        MINUS_1 TYPE F VALUE '-1'. PI     = ACOS( MINUS_1 ).PI_180 = PI / 180. LATITUDE1 = 36,12 . LONGITUDE1 = -86,67 .LATITUDE2 = 33,94 . LONGITUDE2 = -118,4 .   X1 = LATITUDE1  * PI_180.  Y1 = LONGITUDE1 * PI_180.  X2 = LATITUDE2  * PI_180.  Y2 = LONGITUDE2 * PI_180.  YD = Y2 - Y1.   DISTANCE = 20000 / PI *    ACOS( SIN( X1 ) * SIN( X2 ) + COS( X1 ) * COS( X2 ) * COS( YD ) ). WRITE : 'Distance between given points = ' , distance , 'km .' . `
Output:
```Distance between given points = 2.884,2687 km .
```

`with Ada.Text_IO; use Ada.Text_IO;with Ada.Long_Float_Text_IO; use Ada.Long_Float_Text_IO;with Ada.Numerics.Generic_Elementary_Functions; procedure Haversine_Formula is    package Math is new Ada.Numerics.Generic_Elementary_Functions (Long_Float); use Math;    -- Compute great circle distance, given latitude and longitude of two points, in radians   function Great_Circle_Distance (lat1, long1, lat2, long2 : Long_Float) return Long_Float is      Earth_Radius : constant := 6371.0; -- in kilometers      a : Long_Float := Sin (0.5 * (lat2 - lat1));      b : Long_Float := Sin (0.5 * (long2 - long1));   begin      return 2.0 * Earth_Radius * ArcSin (Sqrt (a * a + Cos (lat1) * Cos (lat2) * b * b));   end Great_Circle_Distance;    -- convert degrees, minutes and seconds to radians   function DMS_To_Radians (Deg, Min, Sec : Long_Float := 0.0) return Long_Float is      Pi_Over_180 : constant := 0.017453_292519_943295_769236_907684_886127;   begin      return (Deg + Min/60.0 + Sec/3600.0) * Pi_Over_180;   end DMS_To_Radians; begin   Put_Line("Distance in kilometers between BNA and LAX");   Put (Great_Circle_Distance (         DMS_To_Radians (36.0, 7.2), DMS_To_Radians (86.0, 40.2),       -- Nashville International Airport (BNA)         DMS_To_Radians (33.0, 56.4), DMS_To_Radians (118.0, 24.0)),    -- Los Angeles International Airport (LAX)      Aft=>3, Exp=>0);end Haversine_Formula;`

## ALGOL 68

Translation of: C
Works with: ALGOL 68 version Revision 1.
Works with: ALGOL 68G version Any - tested with release algol68g-2.3.5.
File: Haversine_formula.a68
`#!/usr/local/bin/a68g --script # REAL r = 20 000/pi + 6.6 # km #,     to rad = pi/180; PROC dist = (REAL th1 deg, ph1 deg, th2 deg, ph2 deg)REAL:(        REAL ph1 = (ph1 deg - ph2 deg) * to rad,             th1 = th1 deg * to rad, th2 = th2 deg * to rad,              dz = sin(th1) - sin(th2),             dx = cos(ph1) * cos(th1) - cos(th2),             dy = sin(ph1) * cos(th1);        arc sin(sqrt(dx * dx + dy * dy + dz * dz) / 2) * 2 * r); main:(        REAL d = dist(36.12, -86.67, 33.94, -118.4);        # Americans don't know kilometers #        printf((\$"dist: "g(0,1)" km ("g(0,1)" mi.)"l\$, d, d / 1.609344)))`
Output:
```dist: 2887.3 km (1794.1 mi.)
```

## AMPL

` set location;set geo; param coord{i in location, j in geo};param dist{i in location, j in location}; data; set location := BNA LAX;set geo := LAT LON; param coord:               LAT      LON :=      BNA    36.12   -86.67      LAX    33.94   -118.4; let dist['BNA','LAX'] := 2 * 6372.8 * asin (sqrt(sin(atan(1)/45*(coord['LAX','LAT']-coord['BNA','LAT'])/2)^2 + cos(atan(1)/45*coord['BNA','LAT']) * cos(atan(1)/45*coord['LAX','LAT']) * sin(atan(1)/45*(coord['LAX','LON'] - coord['BNA','LON'])/2)^2)); printf "The distance between the two points is approximately %f km.\n", dist['BNA','LAX']; `
Output:
```The distance between the two points is approximately 2887.259951 km.
```

## APL

`r←6371hf←{(p q)←○⍺ ⍵÷180 ⋄ 2×r×¯1○(+/(2*⍨1○(p-q)÷2)×1(×/2○⊃¨p q))*÷2}36.12 ¯86.67 hf 33.94 ¯118.40`
Output:
`2886.44`

## ATS

` #include"share/atspre_staload.hats" staload "libc/SATS/math.sats"staload _ = "libc/DATS/math.dats"staload "libc/SATS/stdio.sats"staload "libc/SATS/stdlib.sats" #define R 6372.8#define TO_RAD (3.1415926536 / 180) typedef d = double fundist(  th1: d, ph1: d, th2: d, ph2: d) : d = let  val ph1 = ph1 - ph2  val ph1 = TO_RAD * ph1  val th1 = TO_RAD * th1  val th2 = TO_RAD * th2  val dz = sin(th1) - sin(th2)  val dx = cos(ph1) * cos(th1) - cos(th2)  val dy = sin(ph1) * cos(th1)in  asin(sqrt(dx*dx + dy*dy + dz*dz)/2)*2*Rend // end of [dist] implementmain0((*void*)) = let  val d = dist(36.12, ~86.67, 33.94, ~118.4);  /* Americans don't know kilometers */in  \$extfcall(void, "printf", "dist: %.1f km (%.1f mi.)\n", d, d / 1.609344)end // end of [main0] `
Output:
```dist: 2887.3 km (1794.1 mi.)
```

## AutoHotkey

`MsgBox, % GreatCircleDist(36.12, 33.94, -86.67, -118.40, 6372.8, "km") GreatCircleDist(La1, La2, Lo1, Lo2, R, U) {	return, 2 * R * ASin(Sqrt(Hs(Rad(La2 - La1)) + Cos(Rad(La1)) * Cos(Rad(La2)) * Hs(Rad(Lo2 - Lo1)))) A_Space U} Hs(n) {	return, (1 - Cos(n)) / 2} Rad(Deg) {	return, Deg * 4 * ATan(1) / 180}`
Output:
`2887.259951 km`

## AWK

` # syntax: GAWK -f HAVERSINE_FORMULA.AWK# converted from PythonBEGIN {    distance(36.12,-86.67,33.94,-118.40) # BNA to LAX    exit(0)}function distance(lat1,lon1,lat2,lon2,  a,c,dlat,dlon) {    dlat = radians(lat2-lat1)    dlon = radians(lon2-lon1)    lat1 = radians(lat1)    lat2 = radians(lat2)    a = (sin(dlat/2))^2 + cos(lat1) * cos(lat2) * (sin(dlon/2))^2    c = 2 * atan2(sqrt(a),sqrt(1-a))    printf("distance: %.4f km\n",6372.8 * c)}function radians(degree) { # degrees to radians    return degree * (3.1415926 / 180.)} `
Output:
```distance: 2887.2599 km
```

## BBC BASIC

Uses BBC BASIC's MOD(array()) function which calculates the square-root of the sum of the squares of the elements of an array.

`      PRINT "Distance = " ; FNhaversine(36.12, -86.67, 33.94, -118.4) " km"      END       DEF FNhaversine(n1, e1, n2, e2)      LOCAL d() : DIM d(2)      d() = COSRAD(e1-e2) * COSRAD(n1) - COSRAD(n2), \      \     SINRAD(e1-e2) * COSRAD(n1), \      \     SINRAD(n1) - SINRAD(n2)      = ASN(MOD(d()) / 2) * 6372.8 * 2`
Output:
```Distance = 2887.25995 km
```

## C

`#include <stdio.h>#include <stdlib.h>#include <math.h> #define R 6371#define TO_RAD (3.1415926536 / 180)double dist(double th1, double ph1, double th2, double ph2){	double dx, dy, dz;	ph1 -= ph2;	ph1 *= TO_RAD, th1 *= TO_RAD, th2 *= TO_RAD; 	dz = sin(th1) - sin(th2);	dx = cos(ph1) * cos(th1) - cos(th2);	dy = sin(ph1) * cos(th1);	return asin(sqrt(dx * dx + dy * dy + dz * dz) / 2) * 2 * R;} int main(){	double d = dist(36.12, -86.67, 33.94, -118.4);	/* Americans don't know kilometers */	printf("dist: %.1f km (%.1f mi.)\n", d, d / 1.609344); 	return 0;}`

## C++

` #define _USE_MATH_DEFINES #include <math.h>#include <iostream> const static double EarthRadiusKm = 6372.8; inline double DegreeToRadian(double angle){	return M_PI * angle / 180.0;} class Coordinate{public:	Coordinate(double latitude ,double longitude):myLatitude(latitude), myLongitude(longitude)	{} 	double Latitude() const	{		return myLatitude;	} 	double Longitude() const	{		return myLongitude;	} private: 	double myLatitude;	double myLongitude;}; double HaversineDistance(const Coordinate& p1, const Coordinate& p2){	double latRad1 = DegreeToRadian(p1.Latitude());	double latRad2 = DegreeToRadian(p2.Latitude());	double lonRad1 = DegreeToRadian(p1.Longitude());	double lonRad2 = DegreeToRadian(p2.Longitude()); 	double diffLa = latRad2 - latRad1;	double doffLo = lonRad2 - lonRad1; 	double computation = asin(sqrt(sin(diffLa / 2) * sin(diffLa / 2) + cos(latRad1) * cos(latRad2) * sin(doffLo / 2) * sin(doffLo / 2)));	return 2 * EarthRadiusKm * computation;} int main(){	Coordinate c1(36.12, -86.67);	Coordinate c2(33.94, -118.4); 	std::cout << "Distance = " << HaversineDistance(c1, c2) << std::endl;	return 0;} `

## C#

Translation of: Groovy
`public static class Haversine {  public static double calculate(double lat1, double lon1, double lat2, double lon2) {    var R = 6372.8; // In kilometers    var dLat = toRadians(lat2 - lat1);    var dLon = toRadians(lon2 - lon1);    lat1 = toRadians(lat1);    lat2 = toRadians(lat2);     var a = Math.Sin(dLat / 2) * Math.Sin(dLat / 2) + Math.Sin(dLon / 2) * Math.Sin(dLon / 2) * Math.Cos(lat1) * Math.Cos(lat2);    var c = 2 * Math.Asin(Math.Sqrt(a));    return R * 2 * Math.Asin(Math.Sqrt(a));  }   public static double toRadians(double angle) {    return Math.PI * angle / 180.0;  }} void Main() {  Console.WriteLine(String.Format("The distance between coordinates {0},{1} and {2},{3} is: {4}", 36.12, -86.67, 33.94, -118.40, Haversine.calculate(36.12, -86.67, 33.94, -118.40)));} // Returns: The distance between coordinates 36.12,-86.67 and 33.94,-118.4 is: 2887.25995060711 `

## clojure

Translation of: Java
` (defn haversine  [{lon1 :longitude lat1 :latitude} {lon2 :longitude lat2 :latitude}]  (let [R 6372.8 ; kilometers        dlat (Math/toRadians (- lat2 lat1))        dlon (Math/toRadians (- lon2 lon1))        lat1 (Math/toRadians lat1)        lat2 (Math/toRadians lat2)        a (+ (* (Math/sin (/ dlat 2)) (Math/sin (/ dlat 2))) (* (Math/sin (/ dlon 2)) (Math/sin (/ dlon 2)) (Math/cos lat1) (Math/cos lat2)))]    (* R 2 (Math/asin (Math/sqrt a))))) (haversine {:latitude 36.12 :longitude -86.67} {:latitude 33.94 :longitude -118.40});=> 2887.2599506071106 `

## CoffeeScript

Translation of: JavaScript
`haversine = (args...) ->   R = 6372.8; # km  radians = args.map (deg) -> deg/180.0 * Math.PI  lat1 = radians[0]; lon1 = radians[1]; lat2 = radians[2]; lon2 = radians[3]  dLat = lat2 - lat1  dLon = lon2 - lon1  a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.sin(dLon / 2) * Math.sin(dLon / 2) * Math.cos(lat1) * Math.cos(lat2)  R * 2 * Math.asin(Math.sqrt(a)) console.log haversine(36.12, -86.67, 33.94, -118.40)`
Output:
`2887.2599506071124`

## Common Lisp

`(defparameter *earth-radius* 6372.8) (defparameter *rad-conv* (/ pi 180)) (defun deg->rad (x)  (* x *rad-conv*)) (defun haversine (x)  (expt (sin (/ x 2)) 2)) (defun dist-rad (lat1 lng1 lat2 lng2)  (let* ((hlat (haversine (- lat2 lat1)))         (hlng (haversine (- lng2 lng1)))         (root (sqrt (+ hlat (* (cos lat1) (cos lat2) hlng)))))    (* 2 *earth-radius* (asin root)))) (defun dist-deg (lat1 lng1 lat2 lng2)  (dist-rad (deg->rad lat1)            (deg->rad lng1)            (deg->rad lat2)            (deg->rad lng2)))`
Output:
```CL-USER> (format t "~%The distance between BNA and LAX is about ~\$ km.~%"
(dist-deg 36.12 -86.67 33.94 -118.40))

The distance between BNA and LAX is about 2887.26 km.```

## D

`import std.stdio, std.math; real haversineDistance(in real dth1, in real dph1,                       in real dth2, in real dph2)pure nothrow @nogc {    enum real R = 6371;    enum real TO_RAD = PI / 180;     alias imr = immutable real;    imr ph1d = dph1 - dph2;    imr ph1 = ph1d * TO_RAD;    imr th1 = dth1 * TO_RAD;    imr th2 = dth2 * TO_RAD;     imr dz = th1.sin - th2.sin;    imr dx = ph1.cos * th1.cos - th2.cos;    imr dy = ph1.sin * th1.cos;    return asin(sqrt(dx ^^ 2 + dy ^^ 2 + dz ^^ 2) / 2) * 2 * R;} void main() {    writefln("Haversine distance: %.1f km",             haversineDistance(36.12, -86.67, 33.94, -118.4));}`
Output:
`Haversine distance: 2887.3 km`

### Alternative Version

An alternate direct implementation of the haversine formula as shown at wikipedia. The same length, but perhaps a little more clear about what is being done.

`import std.stdio, std.math; real toRad(in real degrees) pure nothrow @safe @nogc {    return degrees * PI / 180;} real haversin(in real theta) pure nothrow @safe @nogc {    return (1 - theta.cos) / 2;} real greatCircleDistance(in real lat1, in real lng1,                         in real lat2, in real lng2,                         in real radius)pure nothrow @safe @nogc {    immutable h = haversin(lat2.toRad - lat1.toRad) +                  lat1.toRad.cos * lat2.toRad.cos *                  haversin(lng2.toRad - lng1.toRad);    return 2 * radius * h.sqrt.asin;} void main() {    enum real earthRadius = 6372.8L; // Average earth radius.     writefln("Great circle distance: %.1f km",             greatCircleDistance(36.12, -86.67, 33.94, -118.4,                                 earthRadius));}`
Output:
```Great circle distance: 2887.3 km
```

## Dart

Translation of: Java
`import 'dart:math'; class Haversine {  static final R = 6372.8; // In kilometers   static double haversine(double lat1, lon1, lat2, lon2) {    double dLat = _toRadians(lat2 - lat1);    double dLon = _toRadians(lon2 - lon1);    lat1 = _toRadians(lat1);    lat2 = _toRadians(lat2);    double a = pow(sin(dLat / 2), 2) + pow(sin(dLon / 2), 2) * cos(lat1) * cos(lat2);    double c = 2 * asin(sqrt(a));    return R * c;  }   static double _toRadians(double degree) {    return degree * pi / 180;  }   static void main() {    print(haversine(36.12, -86.67, 33.94, -118.40));  }} `
Output:
`2887.2599506071106`

## Delphi

`program HaversineDemo;uses Math; function HaversineDist(th1, ph1, th2, ph2:double):double;const diameter = 2 * 6372.8;var   dx, dy, dz:double;begin  ph1    := degtorad(ph1 - ph2);  th1    := degtorad(th1);  th2    := degtorad(th2);   dz     := sin(th1) - sin(th2);  dx     := cos(ph1) * cos(th1) - cos(th2);  dy     := sin(ph1) * cos(th1);  Result := arcsin(sqrt(sqr(dx) + sqr(dy) + sqr(dz)) / 2) * diameter;end; begin  Writeln('Haversine distance: ', HaversineDist(36.12, -86.67, 33.94, -118.4):7:2, ' km.');end.`
Output:
`Haversine distance: 2887.26 km.`

## Elena

ELENA 3.4:

`import extensions.import system'math. Haversine(lat1,lon1,lat2,lon2)[    var R := 6372.8r.    var dLat := (lat2 - lat1) radian.    var dLon := (lon2 - lon1) radian.     var dLat1 := lat1 radian.    var dLat2 := lat2 radian.     var a := (dLat / 2) sin * (dLat / 2) sin + (dLon / 2) sin * (dLon / 2) sin * dLat1 cos * dLat2 cos.     ^ R * 2 * a sqrt; arcsin.] public program[    console printLineFormatted("The distance between coordinates {0},{1} and {2},{3} is: {4}", 36.12r, -86.67r, 33.94r, -118.40r,         Haversine(36.12r, -86.67r, 33.94r, -118.40r))]`
Output:
```The distance between coordinates 36.12,-86.67 and 33.94,-118.4 is: 2887.259950607
```

## Elixir

`defmodule Haversine do  @v  :math.pi / 180  @r  6372.8            # km for the earth radius  def distance({lat1, long1}, {lat2, long2}) do    dlat  = :math.sin((lat2 - lat1) * @v / 2)    dlong = :math.sin((long2 - long1) * @v / 2)    a = dlat * dlat + dlong * dlong * :math.cos(lat1 * @v) * :math.cos(lat2 * @v)    @r * 2 * :math.asin(:math.sqrt(a))  endend bna = {36.12,  -86.67}lax = {33.94, -118.40}IO.puts Haversine.distance(bna, lax)`
Output:
```2887.2599506071106
```

## Elm

`haversine : ( Float, Float ) -> ( Float, Float ) -> Floathaversine ( lat1, lon1 ) ( lat2, lon2 ) =    let        r =            6372.8         dLat =            degrees (lat2 - lat1)         dLon =            degrees (lon2 - lon1)         a =            (sin (dLat / 2))                ^ 2                + (sin (dLon / 2))                ^ 2                * cos (degrees lat1)                * cos (degrees lat2)    in        r * 2 * asin (sqrt a) view =    Html.div []      [ Html.text (toString (haversine ( 36.12, -86.67 ) ( 33.94, -118.4 )))      ] `
Output:
```2887.2599506071106
```

## Erlang

`% Implementer by Arjun Sunel-module(haversine).-export([main/0]). main() ->	haversine(36.12, -86.67, 33.94, -118.40). haversine(Lat1, Long1, Lat2, Long2) ->	V 	         =   math:pi()/180,	R 		 =   6372.8, 	% In kilometers	Diff_Lat 	 =   (Lat2 - Lat1)*V ,		Diff_Long	 =   (Long2 - Long1)*V,		NLat 		 =   Lat1*V,	NLong 		 =   Lat2*V,	A 		 =   math:sin(Diff_Lat/2) * math:sin(Diff_Lat/2) + math:sin(Diff_Long/2) * math:sin(Diff_Long/2) * math:cos(NLat) * math:cos(NLong),	C 		 =   2 * math:asin(math:sqrt(A)),	R*C. `
Output:
```2887.2599506071106
```

## ERRE

`% Implemented by Claudio Larini PROGRAM HAVERSINE_DEMO !\$DOUBLE CONST DIAMETER=12745.6 FUNCTION DEG2RAD(X)    DEG2RAD=X*π/180END FUNCTION FUNCTION RAD2DEG(X)    RAD2DEG=X*180/πEND FUNCTION PROCEDURE HAVERSINE_DIST(TH1,PH1,TH2,PH2->RES)    LOCAL DX,DY,DZ    PH1=DEG2RAD(PH1-PH2)    TH1=DEG2RAD(TH1)    TH2=DEG2RAD(TH2)    DZ=SIN(TH1)-SIN(TH2)    DX=COS(PH1)*COS(TH1)-COS(TH2)    DY=SIN(PH1)*COS(TH1)    RES=ASN(SQR(DX^2+DY^2+DZ^2)/2)*DIAMETEREND PROCEDURE BEGIN    HAVERSINE_DIST(36.12,-86.67,33.94,-118.4->RES)    PRINT("HAVERSINE DISTANCE: ";RES;" KM.")END PROGRAM `

Using double-precision variables output is 2887.260209071741 km, while using single-precision variable output is 2887.261 Km.

## Euler Math Toolbox

Euler has a package for spherical geometry, which is used in the following code. The distances are then computed with the average radius between the two positions. Overwriting the rearth function with the given value yields the known result.

```>load spherical
Spherical functions for Euler.
>esdist(TNA,LAX)->km
2886.48817482
>type esdist
function esdist (frompos: vector, topos: vector)
r1=rearth(frompos[1]);
r2=rearth(topos[1]);
xfrom=spoint(frompos)*r1;
xto=spoint(topos)*r2;
delta=xto-xfrom;
return asin(norm(delta)/(r1+r2))*(r1+r2);
endfunction
>function overwrite rearth (x) := 6372.8*km\$
>esdist(TNA,LAX)->km
2887.25995061
```

## F#

Translation of: Go
using units of measure
`open System [<Measure>] type deg[<Measure>] type rad[<Measure>] type km let haversine (θ: float<rad>) = 0.5 * (1.0 - Math.Cos(θ/1.0<rad>)) let radPerDeg =  (Math.PI / 180.0) * 1.0<rad/deg> type pos(latitude: float<deg>, longitude: float<deg>) =    member this.φ = latitude * radPerDeg    member this.ψ = longitude * radPerDeg let rEarth = 6372.8<km> let hsDist (p1: pos) (p2: pos) =    2.0 * rEarth *        Math.Asin(Math.Sqrt(haversine(p2.φ - p1.φ)+                    Math.Cos(p1.φ/1.0<rad>)*Math.Cos(p2.φ/1.0<rad>)*haversine(p2.ψ - p1.ψ))) [<EntryPoint>]let main argv =    printfn "%A" (hsDist (pos(36.12<deg>, -86.67<deg>)) (pos(33.94<deg>, -118.40<deg>)))    0`
Output:
`2887.259951`

## Factor

Translation of: J
`USING: arrays kernel math math.constants math.functions math.vectors sequences ; : haversin ( x -- y ) cos 1 swap - 2 / ;: haversininv ( y -- x ) 2 * 1 swap - acos ;: haversineDist ( as bs -- d )[ [ 180 / pi * ] map ] [email protected]  [ [ swap - haversin ] 2map ]  [ [ first cos ] [email protected] * 1 swap 2array ]  2biv.haversininv R_earth * ;`
`( scratchpad ) { 36.12 -86.67 } { 33.94 -118.4 } haversineDist .2887.259950607113`

## FBSL

Based on the Fortran and Groovy versions.

`#APPTYPE CONSOLE PRINT "Distance = ", Haversine(36.12, -86.67, 33.94, -118.4), " km"PAUSE FUNCTION Haversine(DegLat1 AS DOUBLE, DegLon1 AS DOUBLE, DegLat2 AS DOUBLE, DegLon2 AS DOUBLE) AS DOUBLE    CONST radius = 6372.8    DIM dLat AS DOUBLE = D2R(DegLat2 - DegLat1)    DIM dLon AS DOUBLE = D2R(DegLon2 - DegLon1)    DIM lat1 AS DOUBLE = D2R(DegLat1)    DIM lat2 AS DOUBLE = D2R(DegLat2)    DIM a AS DOUBLE = SIN(dLat / 2) * SIN(dLat / 2) + SIN(dLon / 2) * SIN(dLon / 2) * COS(lat1) * COS(lat2)    DIM c AS DOUBLE = 2 * ASIN(SQRT(a))    RETURN radius * cEND FUNCTION `
Output:
```Distance = 2887.25995060711 km
Press any key to continue...
```

## Forth

`: s>f s>d d>f ;: deg>rad 174532925199433e-16 f* ;: difference f- deg>rad 2 s>f f/ fsin fdup f* ; : haversine                            ( lat1 lon1 lat2 lon2 -- haversine)  frot difference                      ( lat1 lat2 dLon^2)  frot frot fover fover                ( dLon^2 lat1 lat2 lat1 lat2)  fswap difference                     ( dLon^2 lat1 lat2 dLat^2)  fswap deg>rad fcos                   ( dLon^2 lat1 dLat^2 lat2)  frot  deg>rad fcos f*                ( dLon^2 dLat2 lat1*lat2)  frot  f* f+                          ( lat1*lat2*dLon^2+dLat^2)  fsqrt fasin 127456 s>f f* 10 s>f f/  ( haversine); 36.12e -86.67e 33.94e -118.40e haversine cr f.`
Output:
```2887.25995060711
```

## Fortran

` program exampleimplicit nonereal :: d d = haversine(36.12,-86.67,33.94,-118.40) ! BNA to LAXprint '(A,F9.4,A)', 'distance: ',d,' km' ! distance: 2887.2600 km contains       function to_radian(degree) result(rad)          ! degrees to radians          real,intent(in) :: degree          real, parameter :: deg_to_rad = atan(1.0)/45 ! exploit intrinsic atan to generate pi/180 runtime constant          real :: rad           rad = degree*deg_to_rad      end function to_radian       function haversine(deglat1,deglon1,deglat2,deglon2) result (dist)          ! great circle distance -- adapted from Matlab           real,intent(in) :: deglat1,deglon1,deglat2,deglon2          real :: a,c,dist,dlat,dlon,lat1,lat2          real,parameter :: radius = 6372.8            dlat = to_radian(deglat2-deglat1)          dlon = to_radian(deglon2-deglon1)          lat1 = to_radian(deglat1)          lat2 = to_radian(deglat2)          a = (sin(dlat/2))**2 + cos(lat1)*cos(lat2)*(sin(dlon/2))**2          c = 2*asin(sqrt(a))          dist = radius*c      end function haversine end program example `

## FreeBASIC

`' version 09-10-2016' compile with: fbc -s console ' Nashville International Airport (BNA) in Nashville, TN, USA,' N 36°07.2',  W  86°40.2' (36.12,  -86.67)' Los Angeles International Airport (LAX) in Los Angeles, CA, USA,' N 33°56.4', W 118°24.0'  (33.94, -118.40).' 6372.8 km is an approximation of the radius of the average circumference #Define Pi Atn(1) * 4        ' define Pi = 3.1415..#Define deg2rad Pi / 180     ' define deg to rad 0.01745..#Define earth_radius 6372.8  ' earth radius in km. Function Haversine(lat1 As Double, long1 As Double, lat2 As Double, _                                long2 As Double , radius As Double) As Double   Dim As Double d_long = deg2rad * (long1 - long2)  Dim As Double theta1 = deg2rad * lat1  Dim As Double theta2 = deg2rad * lat2  Dim As Double dx = Cos(d_long) * Cos(theta1) - Cos(theta2)  Dim As Double dy = Sin(d_long) * Cos(theta1)  Dim As Double dz = Sin(theta1) - Sin(theta2)  Return Asin(Sqr(dx*dx + dy*dy + dz*dz) / 2) * radius * 2 End Function PrintPrint " Haversine distance between BNA and LAX = "; _      Haversine(36.12, -86.67, 33.94, -118.4, earth_radius); " km."  ' empty keyboard bufferWhile Inkey <> "" : WendPrint : Print "hit any key to end program"SleepEnd`
Output:
` Haversine distance between BNA and LAX =  2887.259950607111 km.`

## Frink

` haversine[theta] := (1-cos[theta])/2 dist[lat1, long1, lat2, long2] := 2 earthradius arcsin[sqrt[haversine[lat2-lat1] + cos[lat1] cos[lat2] haversine[long2-long1]]] d = dist[36.12 deg, -86.67 deg, 33.94 deg, -118.40 deg]println[d-> "km"] `

Note that physical constants like degrees, kilometers, and the average radius of the earth (as well as the polar and equatorial radii) are already known to Frink. Also note that units of measure are tracked throughout all calculations, and results can be displayed in a huge number of units of distance (miles, km, furlongs, chains, feet, statutemiles, etc.) by changing the final `"km"` to something like `"miles"`.

However, Frink's library/sample program navigation.frink (included in larger distributions) contains a much higher-precision calculation that uses ellipsoidal (not spherical) calculations to determine the distance on earth's geoid with far greater accuracy:

` use navigation.frink d = earthDistance[36.12 deg North, 86.67 deg West, 33.94 deg North, 118.40 deg West]println[d-> "km"] `

## FunL

`import math.* def haversin( theta ) = (1 - cos( theta ))/2 def radians( deg ) = deg Pi/180 def haversine( (lat1, lon1), (lat2, lon2) ) =  R = 6372.8  h = haversin( radians(lat2 - lat1) ) + cos( radians(lat1) ) cos( radians(lat2) ) haversin( radians(lon2 - lon1) )  2R asin( sqrt(h) ) println( haversine((36.12, -86.67), (33.94, -118.40)) )`
Output:
```2887.259950607111
```

## FutureBasic

Note: The Haversine function returns an approximate theoretical value of the Great Circle Distance between two points because it does not factor the ellipsoidal shape of Earth -- fat in the middle from centrifugal force, and squashed at the ends. Navigators once relied on trigonometric functions like versine (versed sine) where angle A is 1-cos(A), and haversine (half versine) or ( 1-cos(A) ) / 2. Also, the radius of the Earth varies, at least depending on who you talk to. Here's NASA's take on it: http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html

Since it was trivial, this functions returns the distance in miles and kilometers.

` include "ConsoleWindow" local fn Haversine( lat1 as double, lon1 as double, lat2 as double, lon2 as double, miles as ^double, kilometers as ^double )dim as double deg2rad, dLat, dLon, a, c, earth_radius_miles, earth_radius_kilometers earth_radius_miles = 3959.0 // Radius of the Earth in milesearth_radius_kilometers = 6372.8 // Radius of the Earth in kilometersdeg2rad = Pi / 180 // Pi is predefined in FutureBasic dLat = deg2rad * ( lat2  - lat1 )  dLon = deg2rad * ( lon2 - lon1 )  a = sin( dLat / 2 ) * sin( dLat / 2 ) + cos( deg2rad * lat1 ) * cos( deg2rad * lat2 ) * sin( dLon / 2 ) * sin( dLon / 2 )  c = 2 * asin( sqr(a) )   miles.nil# =  earth_radius_miles * ckilometers.nil# = earth_radius_kilometers * cend fn dim as double miles, kilometersfn Haversine( 36.12, -86.67, 33.94, -118.4, @miles, @kilometers ) print "Distance in miles between BNA and LAX: "; using "####.####"; miles; " miles."print "Distance in kilometers between BNA LAX: "; using "####.####"; kilometers; " km."  `

Output:

```Distance in miles between BNA and LAX: 1793.6640 miles.
Distance in kilometers between BNA LAX: 2887.2600 km.
```

## Go

`package main import (    "fmt"    "math") func haversine(θ float64) float64 {    return .5 * (1 - math.Cos(θ))} type pos struct {    φ float64 // latitude, radians    ψ float64 // longitude, radians} func degPos(lat, lon float64) pos {    return pos{lat * math.Pi / 180, lon * math.Pi / 180}} const rEarth = 6372.8 // km func hsDist(p1, p2 pos) float64 {    return 2 * rEarth * math.Asin(math.Sqrt(haversine(p2.φ-p1.φ)+        math.Cos(p1.φ)*math.Cos(p2.φ)*haversine(p2.ψ-p1.ψ)))} func main() {    fmt.Println(hsDist(degPos(36.12, -86.67), degPos(33.94, -118.40)))}`
Output:
```2887.2599506071097
```

## Groovy

`def haversine(lat1, lon1, lat2, lon2) {  def R = 6372.8  // In kilometers  def dLat = Math.toRadians(lat2 - lat1)  def dLon = Math.toRadians(lon2 - lon1)  lat1 = Math.toRadians(lat1)  lat2 = Math.toRadians(lat2)   def a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.sin(dLon / 2) * Math.sin(dLon / 2) * Math.cos(lat1) * Math.cos(lat2)  def c = 2 * Math.asin(Math.sqrt(a))  R * c} haversine(36.12, -86.67, 33.94, -118.40) > 2887.25995060711`

`import Text.Printfimport Control.Arrow ((***)) -- The haversine of an angle.haversine :: Float -> Floathaversine = (^ 2) . sin . (/ 2) -- The approximate distance, in kilometers, between two points on Earth.-- The latitude and longtitude are assumed to be in degrees.earthDist :: (Float, Float) -> (Float, Float) -> FloatearthDist = distDeg 6371  where    distDeg radius p1 p2 = distRad radius (deg2rad p1) (deg2rad p2)    distRad radius (lat1, lng1) (lat2, lng2) =      (2 * radius) *      asin        (min           1.0           (sqrt \$            haversine (lat2 - lat1) +            ((cos lat1 * cos lat2) * haversine (lng2 - lng1))))    deg2rad = d2r *** d2r      where        d2r = (/ 180) . (pi *) main :: IO ()main =  printf    "The distance between BNA and LAX is about %0.f km.\n"    (earthDist bna lax)  where    bna = (36.12, -86.67)    lax = (33.94, -118.40)`
Output:
`The distance between BNA and LAX is about 2886 km.`

## Icon and Unicon

Translation of: C
`link printf procedure main()  #: Haversine formula     printf("BNA to LAX is %d km (%d miles)\n",      d := gcdistance([36.12, -86.67],[33.94, -118.40]),d*3280/5280)  # with cute km2mi conversionend procedure gcdistance(a,b)	a[2] -:= b[2]   every (x := a|b)[i := 1 to 2] := dtor(x[i])	dz := sin(a[1]) - sin(b[1])	dx := cos(a[2]) * cos(a[1]) - cos(b[1])	dy := sin(a[2]) * cos(a[1])	return asin(sqrt(dx * dx + dy * dy + dz * dz) / 2) * 2 * 6371end`
Output:
`BNA to LAX is 2886 km (1793 miles)`

## Idris

`module Main -- The haversine of an angle.hsin : Double -> Doublehsin t = let u = sin (t/2) in u*u -- The distance between two points, given by latitude and longtitude, on a-- circle.  The points are specified in radians.distRad : Double -> (Double, Double) -> (Double, Double) -> DoubledistRad radius (lat1, lng1) (lat2, lng2) =  let hlat = hsin (lat2 - lat1)      hlng = hsin (lng2 - lng1)      root = sqrt (hlat + cos lat1 * cos lat2 * hlng)  in 2 * radius * asin (min 1.0 root) -- The distance between two points, given by latitude and longtitude, on a-- circle.  The points are specified in degrees.distDeg : Double -> (Double, Double) -> (Double, Double) -> Double distDeg radius p1 p2 = distRad radius (deg2rad p1) (deg2rad p2)  where         d2r : Double -> Double        d2r t = t * pi / 180         deg2rad (t, u) = (d2r t, d2r u) -- The approximate distance, in kilometers, between two points on Earth.  -- The latitude and longtitude are assumed to be in degrees.earthDist : (Double, Double) -> (Double, Double) -> DoubleearthDist = distDeg 6372.8 main : IO () main = putStrLn \$ "The distance between BNA and LAX is about " ++ show (floor dst) ++ " km." where       bna : (Double, Double)      bna = (36.12,  -86.67)       lax : (Double, Double)      lax = (33.94, -118.40)       dst : Double      dst = earthDist bna lax `
Output:
`The distance between BNA and LAX is about 2887 km.`

## J

Solution:

`require 'trig'haversin=: 0.5 * 1 - cosRearth=: 6372.8haversineDist=: Rearth * haversin^:_1@((1 , *&([email protected]{.)) +/ .* [: haversin -)&rfd `

Note: J derives the inverse haversin ( `haversin^:_1` ) from the definition of haversin.

Example Use:

`   36.12 _86.67 haversineDist 33.94 _118.42887.26`

## Java

Translation of: Groovy
`public class Haversine {    public static final double R = 6372.8; // In kilometers    public static double haversine(double lat1, double lon1, double lat2, double lon2) {        double dLat = Math.toRadians(lat2 - lat1);        double dLon = Math.toRadians(lon2 - lon1);        lat1 = Math.toRadians(lat1);        lat2 = Math.toRadians(lat2);         double a = Math.pow(Math.sin(dLat / 2),2) + Math.pow(Math.sin(dLon / 2),2) * Math.cos(lat1) * Math.cos(lat2);        double c = 2 * Math.asin(Math.sqrt(a));        return R * c;    }    public static void main(String[] args) {        System.out.println(haversine(36.12, -86.67, 33.94, -118.40));    }}`
Output:
`2887.2599506071106`

## JavaScript

### ES5

Translation of: Java
`function haversine() {       var radians = Array.prototype.map.call(arguments, function(deg) { return deg/180.0 * Math.PI; });       var lat1 = radians[0], lon1 = radians[1], lat2 = radians[2], lon2 = radians[3];       var R = 6372.8; // km       var dLat = lat2 - lat1;       var dLon = lon2 - lon1;       var a = Math.sin(dLat / 2) * Math.sin(dLat /2) + Math.sin(dLon / 2) * Math.sin(dLon /2) * Math.cos(lat1) * Math.cos(lat2);       var c = 2 * Math.asin(Math.sqrt(a));       return R * c;}console.log(haversine(36.12, -86.67, 33.94, -118.40));`
Output:
`2887.2599506071124`

### ES6

`((x, y) => {    'use strict';     // haversine :: (Num, Num) -> (Num, Num) -> Num    const haversine = ([lat1, lon1], [lat2, lon2]) => {        // Math lib function names        const [pi, asin, sin, cos, sqrt, pow, round] = [            'PI', 'asin', 'sin', 'cos', 'sqrt', 'pow', 'round'        ]        .map(k => Math[k]),             // degrees as radians            [rlat1, rlat2, rlon1, rlon2] = [lat1, lat2, lon1, lon2]            .map(x => x / 180 * pi),             dLat = rlat2 - rlat1,            dLon = rlon2 - rlon1,            radius = 6372.8; // km         // km        return round(            radius * 2 * asin(                sqrt(                    pow(sin(dLat / 2), 2) +                    pow(sin(dLon / 2), 2) *                    cos(rlat1) * cos(rlat2)                )            ) * 100        ) / 100;    };     // TEST    return haversine(x, y);     // --> 2887.26 })([36.12, -86.67], [33.94, -118.40]);`
Output:
`2887.26`

## jq

`def haversine(lat1;lon1; lat2;lon2):  def radians: . * (1|atan)/45;  def sind: radians|sin;  def cosd: radians|cos;  def sq: . * .;     (((lat2 - lat1)/2) | sind | sq) as \$dlat  | (((lon2 - lon1)/2) | sind | sq) as \$dlon  | 2 * 6372.8 * (( \$dlat + (lat1|cosd) * (lat2|cosd) * \$dlon ) | sqrt | asin) ;`

Example:

```haversine(36.12; -86.67; 33.94; -118.4)
# 2887.2599506071106
```

## Julia

Works with: Julia version 0.6
`haversine(lat1, lon1, lat2, lon2) =    2 * 6372.8 * asin(sqrt(sind((lat2 - lat1) / 2) ^ 2 +    cosd(lat1) * cosd(lat2) * sind((lon2 - lon1) / 2) ^ 2)) @show haversine(36.12, -86.67, 33.94, -118.4)`
Output:
`haversine(36.12, -86.67, 33.94, -118.4) = 2887.2599506071106`

## Kotlin

Translation of: Groovy

Use Unicode characters.

`import java.lang.Math.* const val R = 6372.8 // in kilometers fun haversine(lat1: Double, lon1: Double, lat2: Double, lon2: Double): Double {    val λ1 = toRadians(lat1)    val λ2 = toRadians(lat2)    val Δλ = toRadians(lat2 - lat1)    val Δφ = toRadians(lon2 - lon1)    return 2 * R * asin(sqrt(pow(sin(Δλ / 2), 2.0) + pow(sin(Δφ / 2), 2.0) * cos(λ1) * cos(λ2)))} fun main(args: Array<String>) = println("result: " + haversine(36.12, -86.67, 33.94, -118.40))`

## Liberty BASIC

`print "Haversine distance: "; using( "####.###########", havDist( 36.12, -86.67, 33.94, -118.4)); " km."endfunction havDist( th1, ph1, th2, ph2)  degtorad   = acs(-1)/180  diameter   = 2 * 6372.8    LgD      = degtorad  * (ph1 - ph2)    th1      = degtorad  * th1    th2      = degtorad  * th2    dz       = sin( th1) - sin( th2)    dx       = cos( LgD) * cos( th1) - cos( th2)    dy       = sin( LgD) * cos( th1)    havDist  = asn( ( dx^2 +dy^2 +dz^2)^0.5 /2) *diameterend function`
`Haversine distance: 2887.25995060711  km.`

## LiveCode

`function radians n    return n * (3.1415926 / 180)end radians function haversine lat1, lng1, lat2, lng2    local radiusEarth     local lat3, lng3    local lat1Rad, lat2Rad, lat3Rad    local lngRad1, lngRad2, lngRad3    local haver    put 6372.8 into radiusEarth    put (lat2 - lat1) into lat3    put (lng2 - lng1) into lng3    put radians(lat1) into lat1Rad    put radians(lat2) into lat2Rad    put radians(lat3) into lat3Rad    put radians(lng1) into lngRad1    put radians(lng2) into lngRad2    put radians(lng3) into lngRad3     put (sin(lat3Rad/2.0)^2) + (cos(lat1Rad)) \          * (cos(lat2Rad)) \          * (sin(lngRad3/2.0)^2) \          into haver     return (radiusEarth * (2.0 * asin(sqrt(haver)))) end haversine`

Test

`haversine(36.12, -86.67, 33.94, -118.40)2887.259923`

## Lua

`local function haversine(x1, y1, x2, y2)r=0.017453292519943295769236907684886127;x1= x1*r; x2= x2*r; y1= y1*r; y2= y2*r; dy = y2-y1; dx = x2-x1;a = math.pow(math.sin(dx/2),2) + math.cos(x1) * math.cos(x2) * math.pow(math.sin(dy/2),2); c = 2 * math.asin(math.sqrt(a)); d = 6372.8 * c;return d;end`

Usage:

`print(haversine(36.12, -86.67, 33.94, -118.4));`

Output:

`2887.2599506071`

## Maple

Inputs assumed to be in radians.

`distance := (theta1, phi1, theta2, phi2)->2*6378.14*arcsin( sqrt((1-cos(theta2-theta1))/2 + cos(theta1)*cos(theta2)*(1-cos(phi2-phi1))/2) );`
If you prefer, you can define a haversine function to clarify the definition:
`haversin := theta->(1-cos(theta))/2;distance := (theta1, phi1, theta2, phi2)->2*6378.14*arcsin( sqrt(haversin(theta2-theta1) + cos(theta1)*cos(theta2)*haversin(phi2-phi1)) );`

Usage:

`distance(0.6304129261, -1.512676863, 0.5923647483, -2.066469834)`
Output:
`2889.679287`

## Mathematica / Wolfram Language

Inputs assumed in degrees. Sin and Haversine expect arguments in radians; the built-in variable 'Degree' converts from degrees to radians.

` distance[{theta1_, phi1_}, {theta2_, phi2_}] :=  2*6378.14 [email protected]   Sqrt[Haversine[(theta2 - theta1) Degree] +      Cos[theta1*Degree] Cos[theta2*Degree] Haversine[(phi2 - phi1) Degree]] `

Usage:

`distance[{36.12, -86.67}, {33.94, -118.4}]`
Output:
`2889.68`

## MATLAB / Octave

`function rad = radians(degree) % degrees to radians    rad = degree .* pi / 180;end;  function [a,c,dlat,dlon]=haversine(lat1,lon1,lat2,lon2)% HAVERSINE_FORMULA.AWK - converted from AWK     dlat = radians(lat2-lat1);    dlon = radians(lon2-lon1);    lat1 = radians(lat1);    lat2 = radians(lat2);    a = (sin(dlat./2)).^2 + cos(lat1) .* cos(lat2) .* (sin(dlon./2)).^2;    c = 2 .* asin(sqrt(a));    arrayfun(@(x) printf("distance: %.4f km\n",6372.8 * x), c);end; [a,c,dlat,dlon] = haversine(36.12,-86.67,33.94,-118.40); % BNA to LAX`
Output:
`distance: 2887.2600 km`

## Maxima

`dms(d, m, s) := (d + m/60 + s/3600)*%pi/180\$ great_circle_distance(lat1, long1, lat2, long2) :=   12742*asin(sqrt(sin((lat2 - lat1)/2)^2 + cos(lat1)*cos(lat2)*sin((long2 - long1)/2)^2))\$ /* Coordinates are found here:      http://www.airport-data.com/airport/BNA/      http://www.airport-data.com/airport/LAX/   */ great_circle_distance(dms( 36,  7, 28.10), -dms( 86, 40, 41.50),                      dms( 33, 56, 32.98), -dms(118, 24, 29.05)), numer;/* 2886.326609413624 */`

## MySQL

`DELIMITER \$\$ CREATE FUNCTION haversine (		lat1 FLOAT, lon1 FLOAT,		lat2 FLOAT, lon2 FLOAT	) RETURNS FLOAT	NO SQL DETERMINISTICBEGIN	DECLARE r FLOAT unsigned DEFAULT 6372.8;	DECLARE dLat FLOAT unsigned;	DECLARE dLon FLOAT unsigned;	DECLARE a FLOAT unsigned;	DECLARE c FLOAT unsigned; 	SET dLat = RADIANS(lat2 - lat1);	SET dLon = RADIANS(lon2 - lon1);	SET lat1 = RADIANS(lat1);	SET lat2 = RADIANS(lat2); 	SET a = POW(SIN(dLat / 2), 2) + COS(lat1) * COS(lat2) * POW(SIN(dLon / 2), 2);	SET c = 2 * ASIN(SQRT(a)); 	RETURN (r * c);END\$\$ DELIMITER ;`

Usage:

`SELECT haversine(36.12, -86.67, 33.94, -118.4);`
Output:
`2887.260009765625`

## МК-61/52

`П3	->	П2	->	П1	->	П0пи	1	8	0	/	П4ИП1	МГ	ИП3	МГ	-	ИП4	*	П1	ИП0	МГ	ИП4	*	П0	ИП2	МГ	ИП4	*	П2ИП0	sin	ИП2	sin	-	П8ИП1	cos	ИП0	cos	*	ИП2	cos	-	П6ИП1	sin	ИП0	cos	*	П7ИП6	x^2	ИП7	x^2	ИП8	x^2	+	+	КвКор	2	/	arcsin	2	*	ИП5	*	С/П`

Input: 6371,1 as a radius of the Earth, taken as the ball, or 6367,554 as an average radius of the Earth, or 6367,562 as an approximation of the radius of the average circumference (by Krasovsky's ellipsoid) to Р5; В/О lat1 С/П long1 С/П lat2 С/П long2 С/П; the coordinates must be entered as degrees,minutes (example: 46°50' as 46,5).

Test:

• N 36°7.2', W 86°40.2' - N 33°56.4', W 118°24.0' (Nashville - Los Angeles):
Input: 6371,1 П5 36,072 С/П -86,402 С/П 33,564 С/П -118,24 С/П
Output: 2886,4897.
• N 54°43', E 20°3' - N 43°07', E 131°54' (Kaliningrad - Vladivostok):
Input: 6371,1 П5 54,43 С/П 20,3 С/П 43,07 С/П 131,54 С/П
Output: 7357,4526.

## Nim

`import math proc radians(x): float = x * Pi / 180 proc haversine(lat1, lon1, lat2, lon2): float =  const r = 6372.8 # Earth radius in kilometers  let    dLat = radians(lat2 - lat1)    dLon = radians(lon2 - lon1)    lat1 = radians(lat1)    lat2 = radians(lat2)     a = sin(dLat/2)*sin(dLat/2) + cos(lat1)*cos(lat2)*sin(dLon/2)*sin(dLon/2)    c = 2*arcsin(sqrt(a))   result = r * c echo haversine(36.12, -86.67, 33.94, -118.40)`
Output:
`2.8872599506071115e+03`

## Oberon-2

Works with oo2c version2

` MODULE Haversines;IMPORT   LRealMath,  Out;   PROCEDURE Distance(lat1,lon1,lat2,lon2: LONGREAL): LONGREAL;  CONST    r = 6372.8D0; (* Earth radius as LONGREAL *)    to_radians = LRealMath.pi / 180.0D0;  VAR    d,ph1,th1,th2: LONGREAL;    dz,dx,dy: LONGREAL;  BEGIN    d := lon1 - lon2;    ph1 := d * to_radians;    th1 := lat1 * to_radians;    th2 := lat2 * to_radians;     dz := LRealMath.sin(th1) - LRealMath.sin(th2);    dx := LRealMath.cos(ph1) * LRealMath.cos(th1) - LRealMath.cos(th2);    dy := LRealMath.sin(ph1) * LRealMath.cos(th1);     RETURN LRealMath.arcsin(LRealMath.sqrt(LRealMath.power(dx,2.0) + LRealMath.power(dy,2.0) + LRealMath.power(dz,2.0)) / 2.0) * 2.0 * r;  END Distance;BEGIN  Out.LongRealFix(Distance(36.12,-86.67,33.94,-118.4),6,10);Out.LnEND Haversines. `

Output:

```2887.2602975600
```

## Objeck

` bundle Default {  class Haversine {    function : Dist(th1 : Float, ph1 : Float, th2 : Float, ph2 : Float) ~ Float {      ph1 -= ph2;      ph1 := ph1->ToRadians();      th1 := th1->ToRadians();      th2 := th2->ToRadians();       dz := th1->Sin()- th2->Sin();      dx := ph1->Cos() * th1->Cos() - th2->Cos();      dy := ph1->Sin() * th1->Cos();       return ((dx * dx + dy * dy + dz * dz)->SquareRoot() / 2.0)->ArcSin() * 2 * 6371.0;    }     function : Main(args : String[]) ~ Nil {      IO.Console->Print("distance: ")->PrintLine(Dist(36.12, -86.67, 33.94, -118.4));    }  }} `
Output:
```distance: 2886.44
```

## Objective-C

`+ (double) distanceBetweenLat1:(double)lat1 lon1:(double)lon1                          lat2:(double)lat2 lon2:(double)lon2 {    //degrees to radians    double lat1rad = lat1 * M_PI/180;     double lon1rad = lon1 * M_PI/180;    double lat2rad = lat2 * M_PI/180;    double lon2rad = lon2 * M_PI/180;     //deltas    double dLat = lat2rad - lat1rad;    double dLon = lon2rad - lon1rad;     double a = sin(dLat/2) * sin(dLat/2) + sin(dLon/2) * sin(dLon/2) * cos(lat1rad) * cos(lat2rad);    double c = 2 * asin(sqrt(a));    double R = 6372.8;    return R * c;}`

## OCaml

The core calculation is fairly straightforward, but with an eye toward generality and reuse, this is how I might start:

`(* Preamble -- some math, and an "angle" type which might be part of a common library. *)let pi = 4. *. atan 1.let radians_of_degrees = ( *. ) (pi /. 180.)let haversin theta = 0.5 *. (1. -. cos theta) (* The angle type can track radians or degrees, which I'll use for automatic conversion. *)type angle = Deg of float | Rad of floatlet as_radians = function  | Deg d -> radians_of_degrees d  | Rad r -> r (* Demonstrating use of a module, and record type. *)module LatLong = struct  type t = { lat: float; lng: float }  let of_angles lat lng = { lat = as_radians lat; lng = as_radians lng }  let sub a b = { lat = a.lat-.b.lat; lng = a.lng-.b.lng }   let dist radius a b =    let d = sub b a in    let h = haversin d.lat +. haversin d.lng *. cos a.lat *. cos b.lat in    2. *. radius *. asin (sqrt h)end (* Now we can use the LatLong module to construct coordinates and calculate * great-circle distances. * NOTE radius and resulting distance are in the same measure, and units could * be tracked for this too... but who uses miles? ;) *)let earth_dist = LatLong.dist 6372.8and bna = LatLong.of_angles (Deg 36.12) (Deg (-86.67))and lax = LatLong.of_angles (Deg 33.94) (Deg (-118.4))inearth_dist bna lax;;`

If the above is fed to the REPL, the last line will produce this:

```# earth_dist bna lax;;
- : float = 2887.25995060711102
```

## Oforth

`import: math : haversine(lat1, lon1, lat2, lon2)| lat lon |    lat2 lat1 - asRadian ->lat   lon2 lon1 - asRadian ->lon    lon 2 / sin sq lat1 asRadian cos * lat2 asRadian cos *    lat 2 / sin sq + sqrt asin 2 * 6372.8 * ; haversine(36.12, -86.67, 33.94, -118.40) println`
Output:
```2887.25995060711
```

## ooRexx

Translation of: REXX

The rxmath library provides the required functions.

`/*REXX pgm calculates distance between Nashville & Los Angles airports. */say " Nashville:  north 36º  7.2', west  86º 40.2'   =   36.12º,  -86.67º"say "Los Angles:  north 33º 56.4', west 118º 24.0'   =   33.94º, -118.40º"saydist=surfaceDistance(36.12,  -86.67,  33.94,  -118.4)kdist=format(dist/1       ,,2)         /*show 2 digs past decimal point.*/mdist=format(dist/1.609344,,2)         /*  "  "   "    "     "      "   */ndist=format(mdist*5280/6076.1,,2)     /*  "  "   "    "     "      "   */say ' distance between=  '  kdist  " kilometers,"say '               or   '  mdist  " statute miles,"say '               or   '  ndist  " nautical or air miles."exit                                   /*stick a fork in it, we're done.*//*----------------------------------SURFACEDISTANCE subroutine----------*/surfaceDistance: arg th1,ph1,th2,ph2   /*use haversine formula for dist.*/  radius = 6372.8                      /*earth's mean radius in km      */  ph1 = ph1-ph2  x = cos(ph1) * cos(th1) - cos(th2)  y = sin(ph1) * cos(th1)  z = sin(th1) - sin(th2)  return radius * 2 * aSin(sqrt(x**2+y**2+z**2)/2 ) cos: Return RxCalcCos(arg(1))sin: Return RxCalcSin(arg(1))asin: Return RxCalcArcSin(arg(1),,'R')sqrt: Return RxCalcSqrt(arg(1))::requires rxMath library`
Output:
``` Nashville:  north 36º  7.2', west  86º 40.2'   =   36.12º,  -86.67º
Los Angles:  north 33º 56.4', west 118º 24.0'   =   33.94º, -118.40º

distance between=   2887.26  kilometers,
or    1794.06  statute miles,
or    1559.00  nautical or air miles.```

## PARI/GP

`dist(th1, th2, ph)={  my(v=[cos(ph)*cos(th1)-cos(th2),sin(ph)*cos(th1),sin(th1)-sin(th2)]);  asin(sqrt(norml2(v))/2)};distEarth(th1, ph1, th2, ph2)={  my(d=12742, deg=Pi/180); \\ Authalic diameter of the Earth  d*dist(th1*deg, th2*deg, (ph1-ph2)*deg)};distEarth(36.12, -86.67, 33.94, -118.4)`
Output:
`%1 = 2886.44444`

## Pascal

Works with: Free_Pascal
Library: Math
`Program HaversineDemo(output); uses  Math; function haversineDist(th1, ph1, th2, ph2: double): double;  const   diameter = 2 * 6372.8;  var    dx, dy, dz: double;  begin    ph1 := degtorad(ph1 - ph2);    th1 := degtorad(th1);    th2 := degtorad(th2);     dz := sin(th1) - sin(th2);    dx := cos(ph1) * cos(th1) - cos(th2);    dy := sin(ph1) * cos(th1);    haversineDist := arcsin(sqrt(dx**2 + dy**2 + dz**2) / 2) * diameter;  end; begin  writeln ('Haversine distance: ', haversineDist(36.12, -86.67, 33.94, -118.4):7:2, ' km.');end.`
Output:
```Haversine distance: 2887.26 km.
```

## Perl

Library: ntheory
`use ntheory qw/Pi/; sub asin { my \$x = shift; atan2(\$x, sqrt(1-\$x*\$x)); } sub surfacedist {  my(\$lat1, \$lon1, \$lat2, \$lon2) = @_;  my \$radius = 6372.8;  my \$radians = Pi() / 180;;  my \$dlat = (\$lat2 - \$lat1) * \$radians;  my \$dlon = (\$lon2 - \$lon1) * \$radians;  \$lat1 *= \$radians;  \$lat2 *= \$radians;  my \$a = sin(\$dlat/2)**2 + cos(\$lat1) * cos(\$lat2) * sin(\$dlon/2)**2;  my \$c = 2 * asin(sqrt(\$a));  return \$radius * \$c;} printf "Distance: %.3f km\n", surfacedist(36.12, -86.67, 33.94, -118.4);`
Output:
`Distance: 2887.260 km`

## Perl 6

`class EarthPoint {        has \$.lat; # latitude        has \$.lon; # longitude         has \$earth_radius = 6371; # mean earth radius        has \$radian_ratio = pi / 180;         # accessors for radians        method latR { \$.lat * \$radian_ratio }        method lonR { \$.lon * \$radian_ratio }         method haversine-dist(EarthPoint \$p) {                 my EarthPoint \$arc .= new(                        lat => \$!lat - \$p.lat,                        lon => \$!lon - \$p.lon );                 my \$a = sin(\$arc.latR/2) ** 2 + sin(\$arc.lonR/2) ** 2                        * cos(\$.latR) * cos(\$p.latR);                my \$c = 2 * asin( sqrt(\$a) );                 return \$earth_radius * \$c;        }} my EarthPoint \$BNA .= new(lat => 36.12, lon => -86.67);my EarthPoint \$LAX .= new(lat => 33.94, lon => -118.4); say \$BNA.haversine-dist(\$LAX); # 2886.44444099822`

## Phix

`constant MER = 6371         -- mean earth radius(km)constant DEG_TO_RAD = PI/180 function haversine(atom lat1, long1, lat2, long2)    lat1 *= DEG_TO_RAD    lat2 *= DEG_TO_RAD    long1 *= DEG_TO_RAD    long2 *= DEG_TO_RAD    return MER*arccos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(long2-long1))end function atom d = haversine(36.12,-86.67,33.94,-118.4)printf(1,"Distance is %f km (%f miles)\n",{d,d/1.609344})`
Output:
```Distance is 2886.444443 km (1793.553425 miles)
```

## PHP

`class POI {    private \$latitude;    private \$longitude;    public function __construct(\$latitude, \$longitude) {        \$this->latitude = deg2rad(\$latitude);        \$this->longitude = deg2rad(\$longitude);    }    public function getLatitude() return \$this->latitude;    public function getLongitude() return \$this->longitude;    public function getDistanceInMetersTo(POI \$other) {        \$radiusOfEarth = 6371000;// Earth's radius in meters.        \$diffLatitude = \$other->getLatitude() - \$this->latitude;        \$diffLongitude = \$other->getLongitude() - \$this->longitude;        \$a = sin(\$diffLatitude / 2) * sin(\$diffLatitude / 2) +            cos(\$this->latitude) * cos(\$other->getLatitude()) *            sin(\$diffLongitude / 2) * sin(\$diffLongitude / 2);        \$c = 2 * asin(sqrt(\$a));        \$distance = \$radiusOfEarth * \$c;        return \$distance;    }}`

Test:

`\$user = new POI(\$_GET["latitude"], \$_GET["longitude"]);\$poi = new POI(19,69276, -98,84350); // Piramide del Sol, Mexicoecho \$user->getDistanceInMetersTo(\$poi);`

## PicoLisp

`(scl 12)(load "@lib/math.l") (de haversine (Th1 Ph1 Th2 Ph2)   (setq      Ph1 (*/ (- Ph1 Ph2) pi 180.0)      Th1 (*/ Th1 pi 180.0)      Th2 (*/ Th2 pi 180.0) )   (let      (DX (- (*/ (cos Ph1) (cos Th1) 1.0) (cos Th2))         DY (*/ (sin Ph1) (cos Th1) 1.0)         DZ (- (sin Th1) (sin Th2)) )      (* `(* 2 6371)         (asin            (/               (sqrt (+ (* DX DX) (* DY DY) (* DZ DZ)))               2 ) ) ) ) )`

Test:

`(prinl   "Haversine distance: "   (round (haversine 36.12 -86.67 33.94 -118.4))   " km" )`
Output:
`Haversine distance: 2,886.444 km`

## PL/I

`test: procedure options (main); /* 12 January 2014.  Derived from Fortran version */   declare d float;    d = haversine(36.12, -86.67, 33.94, -118.40);  /* BNA to LAX */   put edit ( 'distance: ', d, ' km') (A, F(10,3)); /* distance: 2887.2600 km */  degrees_to_radians: procedure (degree) returns (float);   declare degree float nonassignable;   declare pi float (15) initial ( (4*atan(1.0d0)) );    return ( degree*pi/180 );end degrees_to_radians; haversine: procedure (deglat1, deglon1, deglat2, deglon2) returns (float);   declare (deglat1, deglon1, deglat2, deglon2) float nonassignable;   declare (a, c, dlat, dlon, lat1, lat2) float;   declare radius float value (6372.8);    dlat = degrees_to_radians(deglat2-deglat1);   dlon = degrees_to_radians(deglon2-deglon1);   lat1 = degrees_to_radians(deglat1);   lat2 = degrees_to_radians(deglat2);   a = (sin(dlat/2))**2 + cos(lat1)*cos(lat2)*(sin(dlon/2))**2;   c = 2*asin(sqrt(a));   return ( radius*c );end haversine; end test;`
Output:
```distance:   2887.260 km
```

## PowerShell

Works with: PowerShell version 3
` Add-Type -AssemblyName System.Device \$BNA = New-Object System.Device.Location.GeoCoordinate 36.12, -86.67\$LAX = New-Object System.Device.Location.GeoCoordinate 33.94, -118.40 \$BNA.GetDistanceTo( \$LAX ) / 1000 `
Output:
```2888.93627213254
```
Works with: PowerShell version 2
` function Get-GreatCircleDistance ( \$Coord1, \$Coord2 )    {    #  Convert decimal degrees to radians    \$Lat1  = \$Coord1[0] / 180 * [math]::Pi    \$Long1 = \$Coord1[1] / 180 * [math]::Pi    \$Lat2  = \$Coord2[0] / 180 * [math]::Pi    \$Long2 = \$Coord2[1] / 180 * [math]::Pi     #  Mean Earth radius (km)    \$R = 6371     #  Haversine formula    \$ArcLength = 2 * \$R *                    [math]::Asin(                        [math]::Sqrt(                            [math]::Sin( ( \$Lat1 - \$Lat2 ) / 2 ) *                            [math]::Sin( ( \$Lat1 - \$Lat2 ) / 2 ) +                            [math]::Cos( \$Lat1 ) *                            [math]::Cos( \$Lat2 ) *                            [math]::Sin( ( \$Long1 - \$Long2 ) / 2 ) *                            [math]::Sin( ( \$Long1 - \$Long2 ) / 2 ) ) )    return \$ArcLength    } \$BNA = 36.12,  -86.67\$LAX = 33.94, -118.40 Get-GreatCircleDistance \$BNA \$LAX `
Output:
```2886.44444283799
```

## Pure Data

Up until now there is no 64bit float in Pure Data, so the result of the calculation might not be completely accurate.

```#N canvas 527 1078 450 686 10;
#X obj 28 427 atan2;
#X obj 28 406 sqrt;
#X obj 62 405 sqrt;
#X obj 28 447 * 2;
#X obj 62 384 -;
#X msg 62 362 1 \\$1;
#X obj 28 339 t f f;
#X obj 28 210 sin;
#X obj 83 207 sin;
#X obj 138 206 cos;
#X obj 193 206 cos;
#X obj 28 179 / 2;
#X obj 83 182 / 2;
#X obj 28 74 unpack f f;
#X obj 28 98 t f f;
#X obj 28 301 expr \$f1 + (\$f2 * \$f3 * \$f4);
#X obj 28 232 t f f;
#X obj 28 257 *;
#X obj 83 232 t f f;
#X obj 83 257 *;
#X obj 83 98 t f b;
#X obj 28 542 * 6372.8;
#X obj 193 120 f 33.94;
#X obj 28 125 - 33.94;
#X msg 28 45 36.12 -86.67;
#X obj 83 123 - -118.4;
#X floatatom 28 577 8 0 0 0 - - -, f 8;
#X connect 0 0 3 0;
#X connect 1 0 0 0;
#X connect 2 0 0 1;
#X connect 3 0 25 0;
#X connect 4 0 2 0;
#X connect 5 0 4 0;
#X connect 6 0 1 0;
#X connect 6 1 5 0;
#X connect 7 0 20 0;
#X connect 8 0 22 0;
#X connect 9 0 15 2;
#X connect 10 0 15 3;
#X connect 11 0 7 0;
#X connect 12 0 8 0;
#X connect 13 0 14 0;
#X connect 13 1 24 0;
#X connect 14 0 27 0;
#X connect 14 1 18 0;
#X connect 15 0 6 0;
#X connect 16 0 11 0;
#X connect 17 0 12 0;
#X connect 18 0 9 0;
#X connect 19 0 10 0;
#X connect 20 0 21 0;
#X connect 20 1 21 1;
#X connect 21 0 15 0;
#X connect 22 0 23 0;
#X connect 22 1 23 1;
#X connect 23 0 15 1;
#X connect 24 0 29 0;
#X connect 24 1 26 0;
#X connect 25 0 30 0;
#X connect 26 0 19 0;
#X connect 27 0 16 0;
#X connect 28 0 13 0;
#X connect 29 0 17 0;
```

## PureBasic

Translation of: Pascal
`#DIA=2*6372.8 Procedure.d Haversine(th1.d,ph1.d,th2.d,ph2.d)  Define dx.d,         dy.d,         dz.d   ph1=Radian(ph1-ph2)  th1=Radian(th1)  th2=Radian(th2)   dz=Sin(th1)-Sin(th2)  dx=Cos(ph1)*Cos(th1)-Cos(th2)  dy=Sin(ph1)*Cos(th1)  ProcedureReturn ASin(Sqr(Pow(dx,2)+Pow(dy,2)+Pow(dz,2))/2)*#DIAEndProcedure OpenConsole("Haversine distance")Print("Haversine distance: ")Print(StrD(Haversine(36.12,-86.67,33.94,-118.4),7)+" km.")Input()`
Output:
`Haversine distance: 2887.2599506 km.`

## Python

`from math import radians, sin, cos, sqrt, asin def haversine(lat1, lon1, lat2, lon2):   R = 6372.8 # Earth radius in kilometers   dLat = radians(lat2 - lat1)  dLon = radians(lon2 - lon1)  lat1 = radians(lat1)  lat2 = radians(lat2)   a = sin(dLat/2)**2 + cos(lat1)*cos(lat2)*sin(dLon/2)**2  c = 2*asin(sqrt(a))   return R * c >>> haversine(36.12, -86.67, 33.94, -118.40)2887.2599506071106>>> `

## R

`dms_to_rad <- function(d, m, s) (d + m / 60 + s / 3600) * pi / 180 # Volumetric mean radius is 6371 km, see http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html# The diameter is thus 12742 km great_circle_distance <- function(lat1, long1, lat2, long2) {   a <- sin(0.5 * (lat2 - lat1))   b <- sin(0.5 * (long2 - long1))   12742 * asin(sqrt(a * a + cos(lat1) * cos(lat2) * b * b))} # Coordinates are found here:#     http://www.airport-data.com/airport/BNA/#     http://www.airport-data.com/airport/LAX/ great_circle_distance(   dms_to_rad(36,  7, 28.10), dms_to_rad( 86, 40, 41.50),   # Nashville International Airport (BNA)   dms_to_rad(33, 56, 32.98), dms_to_rad(118, 24, 29.05))  # Los Angeles International Airport (LAX) # Output:  2886.327`

## Racket

Almost the same as the Scheme version.

` #lang racket(require math)(define earth-radius 6371) (define (distance lat1 long1 lat2 long2)  (define (h a b) (sqr (sin (/ (- b a) 2))))  (* 2 earth-radius      (asin (sqrt (+ (h lat1 lat2)                     (* (cos lat1) (cos lat2) (h long1 long2))))))) (define (deg-to-rad d m s)   (* (/ pi 180) (+ d (/ m 60) (/ s 3600)))) (distance (deg-to-rad 36  7.2 0) (deg-to-rad  86 40.2 0)          (deg-to-rad 33 56.4 0) (deg-to-rad 118 24.0 0)) `
Output:
```2886.444442837984
```

## Raven

Translation of: Groovy
`define PI   -1 acos define toRadians use \$degree  \$degree PI * 180 / define haversine use \$lat1, \$lon1, \$lat2, \$lon2  6372.8 as \$R  # In kilometers  \$lat2 \$lat1 - toRadians   as \$dLat  \$lon2 \$lon1 - toRadians   as \$dLon  \$lat1 toRadians  as \$lat1  \$lat2 toRadians  as \$lat2   \$dLat 2 /  sin   \$dLat 2 /  sin *  \$dLon 2 /  sin  \$dLon 2 /  sin *  \$lat1 cos *   \$lat2 cos * +        as \$a  \$a sqrt  asin  2 *   as \$c  \$R \$c *} -118.40 33.94 -86.67 36.12 haversine "haversine: %.15g\n" print`
Output:
`haversine: 2887.25995060711`

## REXX

The use of normalization for angles isn't required for the Haversine formula, but those normalization functions were included
herein anyway   (to support normalization of input arguments to the trigonometric functions for the general case).

`/*REXX program  calculates  the  distance between  Nashville  and  Los Angles  airports.*/call pi;  numeric digits length(pi)%2            /*use half of decimal digits  of  PI.  */say "       Nashville:  north 36º  7.2', west  86º 40.2'   =   36.12º,  -86.67º"say "      Los Angles:  north 33º 56.4', west 118º 24.0'   =   33.94º, -118.40º"@using_radius= 'using the mean radius of the earth as '            /*a literal for  SAY.*/radii.=.;    radii.1=6372.8;    radii.2=6371     /*mean radii of the earth in kilometers*/say;                         m=1/0.621371192237  /*M:   one statute mile  in      "     */    do radius=1  while radii.radius\==.          /*calc. distance using specific radii. */    d=surfaceDistance( 36.12,    -86.67,    33.94,   -118.4,    radii.radius);         say    say center(@using_radius     radii.radius         ' kilometers', 75, '─')    say ' Distance between:  '   format(d/1            ,,2)    " kilometers,"    say '               or   '   format(d/m            ,,2)    " statute miles,"    say '               or   '   format(d/m*5280/6076.1,,2)    " nautical (or air miles)."    end   /*radius*/                             /*show──┘   2 dec. digs past dec. point*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/Acos: return pi()  *  .5  - aSin( arg(1) )       /*calculate the ArcCos of an argument. */d2d:  return arg(1)               //  360        /*normalize degrees to a  unit circle. */d2r:  return r2r(  arg(1) * pi()  /   180)       /*normalize and convert deg ──► radians*/r2d:  return d2d( (arg(1) * 180   /   pi()))     /*normalize and convert rad ──► degrees*/r2r:  return arg(1)               // (pi() * 2)  /*normalize radians to a  unit circle. */p:    return word( arg(1), 1)                    /*pick the first of two words (numbers)*/pi:   pi=3.141592653589793238462643383279502884197169399375105820975;            return pi/*──────────────────────────────────────────────────────────────────────────────────────*/surfaceDistance: parse arg th1,ph1,th2,ph2,r     /*use  haversine  formula for distance.*/          numeric digits digits() * 2            /*double the number of decimal digits. */             ph1= d2r(ph1 - ph2)                 /*convert degrees ──► radians & reduce.*/             th1= d2r(th1);      th2 =  d2r(th2) /*   "       "     "     "    "    "   */               x= cos(ph1) * cos(th1) - cos(th2)               y= sin(ph1) * cos(th1)               z= sin(th1) - sin(th2)          return Asin( sqrt( x**2 + y**2 + z**2)  / 2 )    *  r  *  2/*──────────────────────────────────────────────────────────────────────────────────────*/Asin: procedure; parse arg x 1 z 1 o 1 p;    a=abs(x);              aa=a * a          if a>=sqrt(2) * .5  then  return sign(x) * Acos( sqrt(1 - aa) )                  do j=2  by 2  until p=z; p=z; o=o*aa* (j-1) /j; z=z + o/(j+1); end /*j*/          return z                               /* [↑]  compute until no more noise.   *//*──────────────────────────────────────────────────────────────────────────────────────*/cos:  procedure; parse arg x;        x=r2r(x);       a=abs(x);                 Hpi=pi * .5          numeric fuzz min(6, digits()  - 3) ;    if a=pi    then return -1          if a=Hpi | a=Hpi*3  then return  0 ;    if a=pi/3  then return .5          if a=pi * 2 / 3     then return -.5;                    return .sinCos(1, 1, -1)/*──────────────────────────────────────────────────────────────────────────────────────*/sin:  procedure; parse arg x;  x=r2r(x);   numeric fuzz min(5, digits() - 3)         if abs(x)=pi  then  return 0;                            return .sinCos(x, x, +1)/*──────────────────────────────────────────────────────────────────────────────────────*/.sinCos: parse arg z 1 p,_,i;  q=x*x            do k=2  by 2; _=-_*q/(k*(k+i)); z=z+_; if z=p  then leave; p=z; end;  return z/*──────────────────────────────────────────────────────────────────────────────────────*/sqrt: procedure; parse arg x; if x=0  then return 0; d=digits(); m.=9; numeric form; h=d+6      numeric digits;  parse value format(x,2,1,,0) 'E0' with g "E" _ .;  g=g * .5'e'_ % 2        do j=0  while h>9;      m.j=h;               h=h%2+1;       end  /*j*/        do k=j+5  to 0  by -1;  numeric digits m.k;  g=(g+x/g)*.5;  end  /*k*/;   return g`

REXX doesn't have most of the higher math functions, so they are included here (above) as subroutines (functions).

```       ╔════════════════════════════════════════════════════════════════════════╗
║ A note on built─in functions:  REXX doesn't have a lot of mathematical ║
║ or  (particularly) trigonometric functions,  so REXX programmers have  ║
║ to write their own.  Usually, this is done once, or most likely,  one  ║
║ is borrowed from another program.  Knowing this, the one that is used  ║
║ has a lot of boilerplate in it.                                        ║
║                                                                        ║
║ Programming note:  the  "general 1─liner"  subroutines are taken from  ║
║ other programs that I wrote, but I broke up their one line of source   ║
║ so it can be viewed without shifting the viewing window.               ║
║                                                                        ║
║ The    pi    constant  (as used here)  is actually a much more robust  ║
║ function and will return up to one million digits in the real version. ║
║                                                                        ║
║ One bad side effect is that, like a automobile without a hood, you see ║
║ all the dirty stuff going on.    Also, don't visit a sausage factory.  ║
╚════════════════════════════════════════════════════════════════════════╝
```
output   when using the in-line defaults:
```       Nashville:  north 36º  7.2', west  86º 40.2'   =   36.12º,  -86.67º
Los Angles:  north 33º 56.4', west 118º 24.0'   =   33.94º, -118.40º

─────────using the mean radius of the earth as  6372.8  kilometers─────────
Distance between:   2887.26  kilometers,
or    1794.06  statute miles,
or    1559.00  nautical (or air miles).

──────────using the mean radius of the earth as  6371  kilometers──────────
Distance between:   2886.44  kilometers,
or    1793.55  statute miles,
or    1558.56  nautical (or air miles).
```

## Ring

` decimals(8)see haversine(36.12, -86.67, 33.94, -118.4) + nl func haversine x1, y1, x2, y2     r=0.01745     x1= x1*r     x2= x2*r     y1= y1*r     y2= y2*r     dy = y2-y1     dx = x2-x1     a = pow(sin(dx/2),2) + cos(x1) * cos(x2) * pow(sin(dy/2),2)     c = 2 * asin(sqrt(a))     d = 6372.8 * c     return d `

## Ruby

`include Math Radius = 6371  # rough radius of the Earth, in kilometers def spherical_distance(start_coords, end_coords)  lat1, long1 = deg2rad *start_coords  lat2, long2 = deg2rad *end_coords  2 * Radius * asin(sqrt(sin((lat2-lat1)/2)**2 + cos(lat1) * cos(lat2) * sin((long2 - long1)/2)**2))end def deg2rad(lat, long)  [lat * PI / 180, long * PI / 180]end bna = [36.12, -86.67]lax = [33.94, -118.4] puts "%.1f" % spherical_distance(bna, lax)`
Output:
`2886.4`

## Run BASIC

`    D2R = atn(1)/45    diam  = 2 * 6372.8Lg1m2  = ((-86.67)-(-118.4)) * D2RLt1    = 36.12 * D2R ' degrees to radLt2    = 33.94 * D2R    dz    = sin(Lt1) - sin(Lt2)    dx    = cos(Lg1m2) * cos(Lt1) - cos(Lt2)    dy    = sin(Lg1m2) * cos(Lt1)    hDist = asn((dx^2 + dy^2 + dz^2)^0.5 /2) * diamprint "Haversine distance: ";using("####.#############",hDist);" km."  'Tips: ( 36 deg 7 min 12 sec ) = print 36+(7/60)+(12/3600).  Produces: 36.12 deg. ' '      http://maps.google.com '      Search   36.12,-86.67 '      Earth. '      Center the pin, zoom airport. '      Directions (destination). '      36.12.-86.66999 '      Distance is 35.37 inches.`
Output
`Haversine distance: 2887.2599506071104 km.`

## Rust

` use std::f64; static R: f64 = 6372.8; fn haversine_dist(mut th1: f64, mut ph1: f64, mut th2: f64, ph2: f64) -> f64 {    ph1 -= ph2;    ph1 = ph1.to_radians();    th1 = th1.to_radians();    th2 = th2.to_radians();    let dz: f64 = th1.sin() - th2.sin();    let dx: f64 = ph1.cos() * th1.cos() - th2.cos();    let dy: f64 = ph1.sin() * th1.cos();    ((dx * dx + dy * dy + dz * dz).sqrt() / 2.0).asin() * 2.0 * R} fn main() {    let d: f64 = haversine_dist(36.12, -86.67, 33.94, -118.4);    println!("Distance: {} km ({} mi)", d, d / 1.609344);}  `
Output
`Distance: 2887.2599506071106 km (1794.060157807846 mi)`

## SAS

` options minoperator; %macro haver(lat1, long1, lat2, long2, type=D, dist=K); 	%if %upcase(&type) in (D DEG DEGREE DEGREES) %then %do;		%let convert = constant('PI')/180;		%end;	%else %if %upcase(&type) in (R RAD RADIAN RADIANS) %then %do;		%let convert = 1;		%end;	%else %do;		%put ERROR - Enter RADIANS or DEGREES for type.;		%goto exit;		%end; 	%if %upcase(&dist) in (M MILE MILES) %then %do;		%let distrat = 1.609344;		%end;	%else %if %upcase(&dist) in (K KM KILOMETER KILOMETERS) %then %do;		%let distrat = 1;		%end;	%else %do;		%put ERROR - Enter M on KM for dist;		%goto exit;		%end; 		data _null_;			convert = &convert;			lat1 = &lat1 * convert;			lat2 = &lat2 * convert;			long1 = &long1 * convert;			long2 = &long2 * convert; 			diff1 = lat2 - lat1;			diff2 = long2 - long1; 			part1 = sin(diff1/2)**2;			part2 = cos(lat1)*cos(lat2);			part3 = sin(diff2/2)**2; 			root = sqrt(part1 + part2*part3); 			dist = 2 * 6372.8 / &distrat * arsin(root); 			put "Distance is " dist "%upcase(&dist)";		run; 	%exit:%mend; %haver(36.12, -86.67, 33.94, -118.40);  `
Output:
`Distance is 2887.2599506 K`

## Scala

`import math._ object Haversine {   val R = 6372.8  //radius in km    def haversine(lat1:Double, lon1:Double, lat2:Double, lon2:Double)={      val dLat=(lat2 - lat1).toRadians      val dLon=(lon2 - lon1).toRadians       val a = pow(sin(dLat/2),2) + pow(sin(dLon/2),2) * cos(lat1.toRadians) * cos(lat2.toRadians)      val c = 2 * asin(sqrt(a))      R * c   }    def main(args: Array[String]): Unit = {      println(haversine(36.12, -86.67, 33.94, -118.40))  }}`
Output:
`2887.2599506071106`

## Scheme

`(define earth-radius 6371)(define pi (acos -1)) (define (distance lat1 long1 lat2 long2)(define (h a b) (expt (sin (/ (- b a) 2)) 2))(* 2 earth-radius (asin (sqrt (+ (h lat1 lat2) (* (cos lat1) (cos lat2) (h long1 long2))))))) (define (deg-to-rad d m s) (* (/ pi 180) (+ d (/ m 60) (/ s 3600)))) (distance (deg-to-rad 36  7.2 0) (deg-to-rad  86 40.2 0)          (deg-to-rad 33 56.4 0) (deg-to-rad 118 24.0 0)); 2886.444442837984`

## Seed7

`\$ include "seed7_05.s7i";  include "float.s7i";  include "math.s7i"; const func float: greatCircleDistance (in float: latitude1, in float: longitude1,    in float: latitude2, in float: longitude2) is func  result    var float: distance is 0.0;  local    const float: EarthRadius is 6372.8;  # Average great-elliptic or great-circle radius in kilometers  begin    distance := 2.0 * EarthRadius * asin(sqrt(sin(0.5 * (latitude2 - latitude1)) ** 2 +                                              cos(latitude1) * cos(latitude2) *                                              sin(0.5 * (longitude2 - longitude1)) ** 2));  end func; const func float: degToRad (in float: degrees) is  return degrees * 0.017453292519943295769236907684886127; const proc: main is func  begin    writeln("Distance in kilometers between BNA and LAX");    writeln(greatCircleDistance(degToRad(36.12), degToRad(-86.67),  # Nashville International Airport (BNA)                                degToRad(33.94), degToRad(-118.4))  # Los Angeles International Airport (LAX)            digits 2);  end func;`
Output:
```2887.26
```

## Sidef

Translation of: Perl 6
`class EarthPoint(lat, lon) {     const earth_radius = 6371       # mean earth radius    const radian_ratio = Num.pi/180     # accessors for radians    method latR { self.lat * radian_ratio }    method lonR { self.lon * radian_ratio }     method haversine_dist(EarthPoint p) {        var arc = EarthPoint(              self.lat - p.lat,              self.lon - p.lon,        )         var a = Math.sum(                  (arc.latR / 2).sin**2,                  (arc.lonR / 2).sin**2 *                    self.latR.cos * p.latR.cos                )         earth_radius * a.sqrt.asin * 2    }} var BNA = EarthPoint.new(lat: 36.12, lon: -86.67)var LAX = EarthPoint.new(lat: 33.94, lon: -118.4) say BNA.haversine_dist(LAX)   #=> 2886.444442837983299747157823945746716...`

## Stata

First, a program to add a distance variable to a dataset, given variables for LAT/LON of two points.

`program spheredist	version 15.0	syntax varlist(min=4 max=4 numeric), GENerate(namelist max=1) ///		[Radius(real 6371) ALTitude(real 0) LABel(string)]	confirm new variable `generate'	local lat1 : word 1 of `varlist'	local lon1 : word 2 of `varlist'	local lat2 : word 3 of `varlist'	local lon2 : word 4 of `varlist'	local r=2*(`radius'+`altitude'/1000)	local k=_pi/180	gen `generate'=`r'*asin(sqrt(sin((`lat2'-`lat1')*`k'/2)^2+ ///		cos(`lat1'*`k')*cos(`lat2'*`k')*sin((`lon2'-`lon1')*`k'/2)^2))	if `"`label'"' != "" {		label variable `generate' `"`label'"'	}end`

Illustration with a sample dataset.

`import delimited airports.csv, clearformat %9.4f l*list      +----------------------------------------------------------------------------------------------------+     | iata                                   airport          city         country       lat         lon |     |----------------------------------------------------------------------------------------------------|  1. |  AMS                Amsterdam Airport Schiphol     Amsterdam     Netherlands   52.3086      4.7639 |  2. |  BNA           Nashville International Airport     Nashville   United States   36.1245    -86.6782 |  3. |  CDG   Charles de Gaulle International Airport         Paris          France   49.0128      2.5500 |  4. |  CGN                      Cologne Bonn Airport       Cologne         Germany   50.8659      7.1427 |  5. |  LAX         Los Angeles International Airport   Los Angeles   United States   33.9425   -118.4080 |     |----------------------------------------------------------------------------------------------------|  6. |  MEM             Memphis International Airport       Memphis   United States   35.0424    -89.9767 |     +----------------------------------------------------------------------------------------------------+`

MEM/CGN joins two Fedex Express hubs. The line AMS/LAX is operated by KLM Royal Dutch Airlines. We will compute the distance between each pair of airports, both at sea level and at typical cruising flight level (35000 ft).

Bear in mind that the actual route of an airliner is usually not a piece of great circle, so this will only give an idea. For instance, according to FlightAware, the route of a Fedex flight from Memphis to Paris is 7852 km long, at FL300 altitude (9150 m). The program given here would yield 7328.33 km instead.

`keep iata lat lonrename (iata lat lon) =2gen k=0tempfile tmpsave "`tmp'"rename *2 *1joinby k using `tmp'drop if iata1>=iata2drop klist      +-----------------------------------------------------------+     | iata1      lat1        lon1   iata2      lat2        lon2 |     |-----------------------------------------------------------|  1. |   AMS   52.3086      4.7639     BNA   36.1245    -86.6782 |  2. |   AMS   52.3086      4.7639     CGN   50.8659      7.1427 |  3. |   AMS   52.3086      4.7639     LAX   33.9425   -118.4080 |  4. |   AMS   52.3086      4.7639     CDG   49.0128      2.5500 |  5. |   AMS   52.3086      4.7639     MEM   35.0424    -89.9767 |     |-----------------------------------------------------------|  6. |   BNA   36.1245    -86.6782     CGN   50.8659      7.1427 |  7. |   BNA   36.1245    -86.6782     CDG   49.0128      2.5500 |  8. |   BNA   36.1245    -86.6782     LAX   33.9425   -118.4080 |  9. |   BNA   36.1245    -86.6782     MEM   35.0424    -89.9767 | 10. |   CDG   49.0128      2.5500     LAX   33.9425   -118.4080 |     |-----------------------------------------------------------| 11. |   CDG   49.0128      2.5500     MEM   35.0424    -89.9767 | 12. |   CDG   49.0128      2.5500     CGN   50.8659      7.1427 | 13. |   CGN   50.8659      7.1427     LAX   33.9425   -118.4080 | 14. |   CGN   50.8659      7.1427     MEM   35.0424    -89.9767 | 15. |   LAX   33.9425   -118.4080     MEM   35.0424    -89.9767 |     +-----------------------------------------------------------+`

Now compute the distances and print the result.

`spheredist lat1 lon1 lat2 lon2, gen(dist) lab(Distance at sea level)spheredist lat1 lon1 lat2 lon2, gen(fl350) alt(10680) lab(Distance at FL350 altitude)format %9.2f dist fl350list iata* dist fl350      +-----------------------------------+     | iata1   iata2      dist     fl350 |     |-----------------------------------|  1. |   AMS     CGN    229.64    230.03 |  2. |   AMS     CDG    398.27    398.94 |  3. |   AMS     MEM   7295.19   7307.56 |  4. |   AMS     BNA   7004.61   7016.48 |  5. |   AMS     LAX   8955.95   8971.13 |     |-----------------------------------|  6. |   BNA     LAX   2886.32   2891.21 |  7. |   BNA     CGN   7222.75   7234.99 |  8. |   BNA     CDG   7018.39   7030.29 |  9. |   BNA     MEM    321.62    322.16 | 10. |   CDG     LAX   9102.51   9117.94 |     |-----------------------------------| 11. |   CDG     CGN    387.82    388.48 | 12. |   CDG     MEM   7317.82   7330.23 | 13. |   CGN     LAX   9185.47   9201.04 | 14. |   CGN     MEM   7514.96   7527.70 | 15. |   LAX     MEM   2599.71   2604.12 |     +-----------------------------------+`

Notice that the distance from Nashville to Los Angeles is given as 2886.32 km, which is slightly different from the task description. The coordinates come from OpenFlights and are supposably more accurate. Using the data in the task description, one gets 2886.44 as expected.

## Swift

Translation of: Objective-C
`import Foundation func haversine(lat1:Double, lon1:Double, lat2:Double, lon2:Double) -> Double {    let lat1rad = lat1 * Double.pi/180    let lon1rad = lon1 * Double.pi/180    let lat2rad = lat2 * Double.pi/180    let lon2rad = lon2 * Double.pi/180     let dLat = lat2rad - lat1rad    let dLon = lon2rad - lon1rad    let a = sin(dLat/2) * sin(dLat/2) + sin(dLon/2) * sin(dLon/2) * cos(lat1rad) * cos(lat2rad)    let c = 2 * asin(sqrt(a))    let R = 6372.8     return R * c} print(haversine(lat1:36.12, lon1:-86.67, lat2:33.94, lon2:-118.40))`
Output:
```2887.25995060711
```

## Tcl

Translation of: Groovy
`package require Tcl 8.5proc haversineFormula {lat1 lon1 lat2 lon2} {    set rads [expr atan2(0,-1)/180]    set R 6372.8    ;# In kilometers     set dLat [expr {(\$lat2-\$lat1) * \$rads}]    set dLon [expr {(\$lon2-\$lon1) * \$rads}]    set lat1 [expr {\$lat1 * \$rads}]    set lat2 [expr {\$lat2 * \$rads}]     set a [expr {sin(\$dLat/2)**2 + sin(\$dLon/2)**2*cos(\$lat1)*cos(\$lat2)}]    set c [expr {2*asin(sqrt(\$a))}]    return [expr {\$R * \$c}]} # Don't bother with too much inappropriate accuracy!puts [format "distance=%.1f km" [haversineFormula 36.12 -86.67 33.94 -118.40]]`
Output:
`distance=2887.3 km`

## TechBASIC

` FUNCTION HAVERSINE!---------------------------------------------------------------!*** Haversine Formula - Calculate distances by LAT/LONG! !*** LAT/LON of the two locations and Unit of measure are GLOBAL!*** as they are defined in the main logic of the program, so they!*** available for use in the Function.!*** Usage: X=HAVERSINE      Radius=6378.137    Lat1=(Lat1*MATH.PI/180)    Lon1=(Lon1*MATH.PI/180)    Lat2=(Lat2*MATH.PI/180)    Lon2=(Lon2*MATH.PI/180)    DLon=Lon1-Lon2    ANSWER=ACOS(SIN(Lat1)*SIN(Lat2)+COS(Lat1)*COS(Lat2)*COS(DLon))*Radius     DISTANCE="kilometers"    SELECT CASE UNIT           CASE "M"                HAVERSINE=ANSWER*0.621371192                Distance="miles"           CASE "N"                HAVERSINE=ANSWER*0.539956803                Distance="nautical miles"    END SELECT        END FUNCTION `

The following is the main code that invokes the function. It takes your location and determines how far away you are from Tampa, Florida. You can change UNIT to either M=Miles, N=Nautical Miles, or K (or leave blank) as default is in Kilometers:

```!*** In techBASIC, all variables defined in the main program act as GLOBAL
!*** variables and are available to all SUBROUTINES and FUNCTIONS. So in the
!*** HAVERSINE Function being used, no paramaters need to be passed to it, so
!*** it acts as a variable when I use it as Result=HAVERSINE. The way that
!*** the Function is setup, it returns its value back as HAVERSINE.

BASE 1

!*** Get the GPS LAT/LONG of current location
location = sensors.location(30)
Lat1=location(1)
Lon1=location(2)

!*** LAT/LONG For Tampa, FL
Lat2=27.9506
Lon2=-82.4572

!*** Units: K=kilometers  M=miles  N=nautical miles
DIM UNIT      AS STRING
DIM Distance  AS STRING
DIM Result    AS SINGLE
UNIT = "M"

!*** Calculate distance using Haversine Function
Result=HAVERSINE

PRINT "The distance from your current location to Tampa, FL in ";Distance;" is: ";
PRINT USING "#,###.##";Result;"."

STOP
```

OUTPUT: *** NOTE: When I run this, I am in my house in Venice, Florida, and that distance is correct (as the crow flies). ***

```The distance from your current location to Tampa, FL in miles is:    57.94
```

` # syntax: CALL SP_HAVERSINE(36.12,33.94,-86.67,-118.40,x); CREATE PROCEDURE SP_HAVERSINE(IN lat1 FLOAT,IN lat2 FLOAT,IN lon1 FLOAT,IN lon2 FLOAT,OUT distance FLOAT) BEGIN     DECLARE dLat FLOAT;    DECLARE dLon FLOAT;    DECLARE c FLOAT;    DECLARE a FLOAT;        DECLARE km FLOAT;     SET dLat = RADIANS(lat2-lat1);    SET dLon = RADIANS(lon2-lon1);     SET a = SIN(dLat / 2) * SIN(dLat / 2) + SIN(dLon / 2) * SIN(dLon / 2) * COS(RADIANS(lat1)) * COS(RADIANS(lat2));    SET c = 2 * ASIN(SQRT(a));    SET km = 6372.8 * c;     SELECT km INTO distance;END; `
Output:
```distance: 2887.2599 km
```

## T-SQL

Translation of: C#
`CREATE FUNCTION [dbo].[Haversine](@Lat1 AS DECIMAL(9,7), @Lon1 AS DECIMAL(10,7), @Lat2 AS DECIMAL(9,7), @Lon2 AS DECIMAL(10,7))RETURNS DECIMAL(12,7)ASBEGIN	DECLARE @R	DECIMAL(11,7);	DECLARE @dLat	DECIMAL(9,7);	DECLARE @dLon	DECIMAL(10,7);	DECLARE @a	DECIMAL(10,7);	DECLARE @c	DECIMAL(10,7); 	SET @R		= 6372.8;	SET @dLat	= RADIANS(@Lat2 - @Lat1);	SET @dLon	= RADIANS(@Lon2 - @Lon1);	SET @Lat1	= RADIANS(@Lat1);	SET @Lat2	= RADIANS(@Lat2);	SET @a		= SIN(@dLat / 2) * SIN(@dLat / 2) + SIN(@dLon / 2) * SIN(@dLon / 2) * COS(@Lat1) * COS(@Lat2);	SET @c		= 2 * ASIN(SQRT(@a)); 	RETURN @R * @c;ENDGO SELECT dbo.Haversine(36.12,-86.67,33.94,-118.4) `
Output:
``` 2887.2594934
```

## UBASIC

`    10  Point 7    'Sets decimal display to 32 places (0+.1^56)   20  Rf=#pi/180 'Degree -> Radian Conversion  100 ?Using(,7),.DxH(36+7.2/60,-(86+40.2/60),33+56.4/60,-(118+24/60));" km"  999  End 1000 '*** Haversine Distance Function *** 1010 .DxH(Lat_s,Long_s,Lat_f,Long_f) 1020  L_s=Lat_s*rf:L_f=Lat_f*rf:LD=L_f-L_s:MD=(Long_f-Long_s)*rf 1030  Return(12745.6*asin( (sin(.5*LD)^2+cos(L_s)*cos(L_f)*sin(.5*MD)^2)^.5)) '' ''  Run  2887.2599506 km OK `

## X86 Assembly

Assemble with tasm /m /l; tlink /t

`0000                                 .model  tiny0000                                 .code                                     .486                                     org     100h            ;.com files start here0100  9B DB E3               start:  finit                   ;initialize floating-point unit (FPU)                             ;Great circle distance =                             ; 2.0*Radius * ASin( sqrt( Haversine(Lat2-Lat1) +                             ;                          Haversine(Lon2-Lon1)*Cos(Lat1)*Cos(Lat2) ) )0103  D9 06 0191r                    fld     Lat2            ;push real onto FPU stack0107  D8 26 018Dr                    fsub    Lat1            ;subtract real from top of stack (st(0) = st)010B  E8 0070                        call    Haversine       ;(1.0-cos(st)) / 2.0010E  D9 06 0199r                    fld     Lon2            ;repeat for longitudes0112  D8 26 0195r                    fsub    Lon10116  E8 0065                        call    Haversine       ;st(1)=Lats; st=Lons0119  D9 06 018Dr                    fld     Lat1011D  D9 FF                          fcos                    ;replace st with its cosine011F  D9 06 0191r                    fld     Lat20123  D9 FF                          fcos            ;st=cos(Lat2); st(1)=cos(Lat1); st(2)=Lats; st(3)=Lons0125  DE C9                          fmul            ;st=cos(Lat2)*cos(Lat1); st(1)=Lats; st(2)=Lons0127  DE C9                          fmul            ;st=cos(Lat2)*cos(Lat1)*Lats; st(1)=Lons0129  DE C1                          fadd            ;st=cos(Lat2)*cos(Lat1)*Lats + Lons012B  D9 FA                          fsqrt                   ;replace st with its square root                             ;asin(x) = atan(x/sqrt(1-x^2))012D  D9 C0                          fld     st              ;duplicate tos012F  D8 C8                          fmul    st, st          ;x^20131  D9 E8                          fld1                    ;get 1.00133  DE E1                          fsubr                   ;1 - x^20135  D9 FA                          fsqrt                   ;sqrt(1-x^2)0137  D9 F3                          fpatan                  ;take atan(st(1)/st)0139  D8 0E 019Dr                    fmul    Radius2         ;*2.0*Radius                              ;Display value in FPU's top of stack (st)      =0004                  before  equ     4               ;places before      =0002                  after   equ     2               ; and after decimal point      =0001                  scaler  =       1               ;"=" allows scaler to be redefined, unlike equ                                     rept    after           ;repeat block "after" times                             scaler  =       scaler*10                                     endm                    ;scaler now = 10^after 013D  66| 6A 64                      push    dword ptr scaler;use stack for convenient memory location0140  67| DA 0C 24                   fimul   dword ptr [esp] ;st:= st*scaler0144  67| DB 1C 24                   fistp   dword ptr [esp] ;round st to nearest integer0148  66| 58                         pop     eax             ; and put it into eax 014A  66| BB 0000000A                mov     ebx, 10         ;set up for idiv instruction0150  B9 0006                        mov     cx, before+after;set up loop counter0153  66| 99                 ro10:   cdq                     ;convert double to quad; i.e: edx:= 00155  66| F7 FB                      idiv    ebx             ;eax:= edx:eax/ebx; remainder in edx0158  52                             push    dx              ;save least significant digit on stack0159  E2 F8                          loop    ro10            ;cx--; loop back if not zero 015B  B1 06                          mov     cl, before+after;(ch=0)015D  B3 00                          mov     bl, 0           ;used to suppress leading zeros015F  58                     ro20:   pop     ax              ;get digit0160  0A D8                          or      bl, al          ;turn off suppression if not a zero0162  80 F9 03                       cmp     cl, after+1     ;is digit immediately to left of decimal point?0165  75 01                          jne     ro30            ;skip if not0167  43                              inc    bx              ;turn off leading zero suppression0168  04 30                  ro30:   add     al, '0'         ;if leading zero then ' ' else add 0016A  84 DB                          test    bl, bl016C  75 02                          jne     ro40016E  B0 20                           mov    al, ' '0170  CD 29                  ro40:   int     29h             ;display character in al register0172  80 F9 03                       cmp     cl, after+1     ;is digit immediately to left of decimal point?0175  75 04                          jne     ro50            ;skip if not0177  B0 2E                           mov    al, '.'         ;display decimal point0179  CD 29                           int    29h017B  E2 E2                  ro50:   loop    ro20            ;loop until all digits displayed017D  C3                             ret                     ;return to OS 017E                         Haversine:                      ;return (1.0-Cos(Ang)) / 2.0 in st017E  D9 FF                          fcos0180  D9 E8                          fld10182  DE E1                          fsubr0184  D8 36 0189r                    fdiv    N20188  C3                             ret 0189  40000000               N2      dd       2.0018D  3F21628D               Lat1    dd       0.63041        ;36.12*pi/1800191  3F17A4E8               Lat2    dd       0.59236        ;33.94*pi/1800195  BFC19F80               Lon1    dd      -1.51268        ;-86.67*pi/1800199  C004410B               Lon2    dd      -2.06647        ;-118.40*pi/180019D  46472666               Radius2 dd      12745.6         ;6372.8 average radius of Earth (km) times 2                             ;(TASM isn't smart enough to do floating point constant calculations)                                     end     start `
Output:
```2887.25
```

## XPL0

`include c:\cxpl\codes;                  \intrinsic 'code' declarations func real Haversine(Ang);real Ang;return (1.0-Cos(Ang)) / 2.0; func real Dist(Lat1, Lat2, Lon1, Lon2); \Great circle distancereal Lat1, Lat2, Lon1, Lon2;def R = 6372.8;                         \average radius of Earth (km)return 2.0*R * ASin( sqrt( Haversine(Lat2-Lat1) +       Cos(Lat1)*Cos(Lat2)*Haversine(Lon2-Lon1) )); def D2R = 3.141592654/180.0;            \degrees to radiansRlOut(0, Dist(36.12*D2R, 33.94*D2R, -86.67*D2R, -118.40*D2R ));`
Output:
``` 2887.25995
```

## XQuery

`declare namespace xsd = "http://www.w3.org/2001/XMLSchema";declare namespace math = "http://www.w3.org/2005/xpath-functions/math"; declare function local:haversine(\$lat1 as xsd:float, \$lon1 as xsd:float, \$lat2 as xsd:float, \$lon2 as xsd:float)    as xsd:float{    let \$dlat  := (\$lat2 - \$lat1) * math:pi() div 180    let \$dlon  := (\$lon2 - \$lon1) * math:pi() div 180    let \$rlat1 := \$lat1 * math:pi() div 180    let \$rlat2 := \$lat2 * math:pi() div 180    let \$a     := math:sin(\$dlat div 2) * math:sin(\$dlat div 2) + math:sin(\$dlon div 2) * math:sin(\$dlon div 2) * math:cos(\$rlat1) * math:cos(\$rlat2)    let \$c     := 2 * math:atan2(math:sqrt(\$a), math:sqrt(1-\$a))    return xsd:float(\$c * 6371.0)}; local:haversine(36.12, -86.67, 33.94, -118.4)`
Output:
``` 2886.444
```

## zkl

Translation of: Erlang
`haversine(36.12, -86.67, 33.94, -118.40).println(); fcn haversine(Lat1, Long1, Lat2, Long2){   const R = 6372.8; 	// In kilometers;   Diff_Lat  := (Lat2  - Lat1) .toRad();   Diff_Long := (Long2 - Long1).toRad();   NLat      := Lat1.toRad();   NLong     := Lat2.toRad();   A 	     := (Diff_Lat/2) .sin().pow(2) +                 (Diff_Long/2).sin().pow(2) * 		NLat.cos() * NLong.cos();   C 	     := 2.0 * A.sqrt().asin();   R*C;}`
Output:
```2887.26
```

## ZX Spectrum Basic

Translation of: Run_BASIC
`10 LET diam=2*6372.820 LET Lg1m2=FN r((-86.67)-(-118.4))30 LET Lt1=FN r(36.12)40 LET Lt2=FN r(33.94)50 LET dz=SIN (Lt1)-SIN (Lt2)60 LET dx=COS (Lg1m2)*COS (Lt1)-COS (Lt2)70 LET dy=SIN (Lg1m2)*COS (Lt1)80 LET hDist=ASN ((dx*dx+dy*dy+dz*dz)^0.5/2)*diam90 PRINT "Haversine distance: ";hDist;" km."100 STOP 1000 DEF FN r(a)=a*0.017453293: REM convert degree to radians`