In my article a few years ago (link: http://www.codeproject.com/Articles/469500/Edumatter-School-Math-Calculators-and-Equation-Sol ) I described 3 useful Functions for calculating the distance between 2 geo -points (in other words, a large circular (orthodromic) distance on Earth between 2 geo-points), which differs in terms of accuracy / performance:
// Haversine formula to calculate great-circle distance between two points on Earth private const double _radiusEarthMiles = 3959; private const double _radiusEarthKM = 6371; private const double _m2km = 1.60934; private const double _toRad = Math.PI / 180; /// <summary> /// Haversine formula to calculate /// great-circle (orthodromic) distance on Earth /// High Accuracy, Medium speed /// </summary> /// <param name="Lat1">double: 1st point Latitude</param> /// <param name="Lon1">double: 1st point Longitude</param> /// <param name="Lat2">double: 2nd point Latitude</param> /// <param name="Lon2">double: 2nd point Longitude</param> /// <returns>double: distance in miles</returns> public static double DistanceMilesHaversine(double Lat1, double Lon1, double Lat2, double Lon2) { try { double _radLat1 = Lat1 * _toRad; double _radLat2 = Lat2 * _toRad; double _dLatHalf = (_radLat2 - _radLat1) / 2; double _dLonHalf = Math.PI * (Lon2 - Lon1) / 360; // intermediate result double _a = Math.Sin(_dLatHalf); _a *= _a; // intermediate result double _b = Math.Sin(_dLonHalf); _b *= _b * Math.Cos(_radLat1) * Math.Cos(_radLat2); // central angle, aka arc segment angular distance double _centralAngle = 2 * Math.Atan2(Math.Sqrt(_a + _b), Math.Sqrt(1 - _a - _b)); // great-circle (orthodromic) distance on Earth between 2 points return _radiusEarthMiles * _centralAngle; } catch { throw; } } // Spherical law of cosines formula to calculate great-circle distance between two points on Earth /// <summary> /// Spherical Law of Cosines formula to calculate /// great-circle (orthodromic) distance on Earth; /// High Accuracy, Medium speed /// http://en.wikipedia.org/wiki/Spherical_law_of_cosines /// </summary> /// <param name="Lat1">double: 1st point Latitude</param> /// <param name="Lon1">double: 1st point Longitude</param> /// <param name="Lat2">double: 2nd point Latitude</param> /// <param name="Lon2">double: 2nd point Longitude</param> /// <returns>double: distance in miles</returns> public static double DistanceMilesSLC( double Lat1, double Lon1, double Lat2, double Lon2) { try { double _radLat1 = Lat1 * _toRad; double _radLat2 = Lat2 * _toRad; double _radLon1 = Lon1 * _toRad; double _radLon2 = Lon2 * _toRad; // central angle, aka arc segment angular distance double _centralAngle = Math.Acos(Math.Sin(_radLat1) * Math.Sin(_radLat2) + Math.Cos(_radLat1) * Math.Cos(_radLat2) * Math.Cos(_radLon2 - _radLon1)); // great-circle (orthodromic) distance on Earth between 2 points return _radiusEarthMiles * _centralAngle; } catch { throw; } } // Great-circle distance calculation using Spherical Earth projection formula** /// <summary> /// Spherical Earth projection to a plane formula (using Pythagorean Theorem) /// to calculate great-circle (orthodromic) distance on Earth. /// http://en.wikipedia.org/wiki/Geographical_distance /// central angle = /// Sqrt((_radLat2 - _radLat1)^2 + (Cos((_radLat1 + _radLat2)/2) * (Lon2 - Lon1))^2) /// Medium Accuracy, Fast, /// relative error less than 0.1% in search area smaller than 250 miles /// </summary> /// <param name="Lat1">double: 1st point Latitude</param> /// <param name="Lon1">double: 1st point Longitude</param> /// <param name="Lat2">double: 2nd point Latitude</param> /// <param name="Lon2">double: 2nd point Longitude</param> /// <returns>double: distance in miles</returns> public static double DistanceMilesSEP(double Lat1, double Lon1, double Lat2, double Lon2) { try { double _radLat1 = Lat1 * _toRad; double _radLat2 = Lat2 * _toRad; double _dLat = (_radLat2 - _radLat1); double _dLon = (Lon2 - Lon1) * _toRad; double _a = (_dLon) * Math.Cos((_radLat1 + _radLat2) / 2); // central angle, aka arc segment angular distance double _centralAngle = Math.Sqrt(_a * _a + _dLat * _dLat); // great-circle (orthodromic) distance on Earth between 2 points return _radiusEarthMiles * _centralAngle; } catch { throw; } }
Functions return results in miles; to find the distance in km, multiply the result by 1.60934 (see private const double _m2km = 1.60934 ).
Regarding the sample: find the distance point1 (36.578581, -118.291994) and point 2 (36.23998, -116.83171), the three above-mentioned functions produced the following results (km):
136.00206654936932 136.00206654937023 136.00374497149613
and a calculator (link: http://www.movable-type.co.uk/scripts/latlong.html ) gave the result: 136.0
Hope this helps. Best wishes,