# Vincenty vs Haversine Distance Calculations

## JavaScript performance comparison

Test case created by Drew Robinson

## Info

This test compares JavaScript implementations of the two main different point-to-point distance calculation equations, Haversine and Vincenty.

Among geodetics enthusiasts, Haversine is perhaps slightly looked-down upon because its accuracy can be out by 0.3% or so, whereas Vincenty is apparently accurate to 0.5mm. Of course, both methods use a theoretical spheroid, and because no-one can actually travel on either theoretical spheroid, both are only an approximation :-)

## Preparation code

`` <script>  Benchmark.prototype.setup = function() {    /** Converts numeric degrees to radians */    if (typeof(Number.prototype.toRad) === "undefined") {      Number.prototype.toRad = function() {        return this * Math.PI / 180;      }    }        /**     * Calculates geodetic distance between two points specified by latitude/longitude using      * Vincenty inverse formula for ellipsoids     *     * @param   {Number} lat1, lon1: first point in decimal degrees     * @param   {Number} lat2, lon2: second point in decimal degrees     * @returns (Number} distance in metres between points     */        function distVincenty(lat1, lon1, lat2, lon2) {      var a = 6378137,          b = 6356752.314245,          f = 1 / 298.257223563; // WGS-84 ellipsoid params      var L = (lon2 - lon1).toRad();      var U1 = Math.atan((1 - f) * Math.tan(lat1.toRad()));      var U2 = Math.atan((1 - f) * Math.tan(lat2.toRad()));      var sinU1 = Math.sin(U1),          cosU1 = Math.cos(U1);      var sinU2 = Math.sin(U2),          cosU2 = Math.cos(U2);          var lambda = L,          lambdaP, iterLimit = 100;      do {        var sinLambda = Math.sin(lambda),            cosLambda = Math.cos(lambda);        var sinSigma = Math.sqrt((cosU2 * sinLambda) * (cosU2 * sinLambda) + (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) * (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));        if (sinSigma == 0) return 0; // co-incident points        var cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;        var sigma = Math.atan2(sinSigma, cosSigma);        var sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;        var cosSqAlpha = 1 - sinAlpha * sinAlpha;        var cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;        if (isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)        var C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));        lambdaP = lambda;        lambda = L + (1 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));      } while (Math.abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0);          if (iterLimit == 0) return NaN // formula failed to converge      var uSq = cosSqAlpha * (a * a - b * b) / (b * b);      var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));      var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));      var deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));      var s = b * A * (sigma - deltaSigma);          s = s.toFixed(3); // round to 1mm precision      return s;    }        // Distance in kilometers between two points using the Haversine algo.    function haversine(lat1, lon1, lat2, lon2) {      var R = 6371;      var dLat = (lat2 - lat1).toRad();      var dLong = (lon2 - lon1).toRad();          var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) * Math.sin(dLong / 2) * Math.sin(dLong / 2);      var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));      var d = R * c;          return Math.round(d);    }  };</script>``

## Test runner

Warning! For accurate results, please disable Firebug before running the tests. (Why?)

Java applet disabled.

Testing in unknown unknown
Test Ops/sec
Vincenty formula
``distVincenty(-31.965379, 115.822077, -33.85789, 151.214806);``
pending…
Haversine formula
``haversine(-31.965379, 115.822077, -33.85789, 151.214806);``
pending…

## Revisions

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