Calculate distance between 2 GPS coordinates

Question

How do I calculate distance between two GPS coordinates  using latitude and longitude

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Maybe a typo error   We have an unused variable dlon in GetDirection  I assume   double y   Math Sin dlon    Math Cos lat2      cannot use degrees in Cos     should be   double y   Math Sin dlon    Math Cos dlat

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This is very easy to do with geography type in SQL Server 2008   SELECT geography  Point lat1  lon1  4326  STDistance geography  Point lat2  lon2  4326   -- computes distance in meters using eliptical model  accurate to the mm   4326 is SRID for WGS84 elipsoidal Earth model

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you can find a implementation of this  with some good explanation  in F  on fssnip  here are the important parts    let GreatCircleDistance lt  ltMeasure gt   u gt  R   float lt u gt   p1   Location   p2   Location        let degToRad  x   float ltdeg gt    System Math PI   x   180 0 ltdeg rad gt      let sq x   x   x        take the sin of the half and square the result     let sinSqHf  a   float ltrad gt     System Math Sin  gt gt sq   a   2 0 ltrad gt      let cos  a   float ltdeg gt    System Math Cos  degToRad a   1 0 ltrad gt       let dLat    p2 Latitude - p1 Latitude    gt degToRad     let dLon    p2 Longitude - p1 Longitude    gt degToRad      let a   sinSqHf dLat   cos p1 Latitude   cos p2 Latitude   sinSqHf dLon     let c   2 0   System Math Atan2 System Math Sqrt a   System Math Sqrt 1 0-a        R   c

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i took the top answer and used it in a Scala program  import java lang Math  atan2  cos  sin  sqrt   def latLonDistance lat1  Double  lon1  Double  lat2  Double  lon2  Double   Double         val earthRadiusKm   6371     val dLat    lat2 - lat1  toRadians     val dLon    lon2 - lon1  toRadians     val latRad1   lat1 toRadians     val latRad2   lat2 toRadians      val a   sin dLat   2    sin dLat   2    sin dLon   2    sin dLon   2    cos latRad1    cos latRad2      val c   2   atan2 sqrt a   sqrt 1 - a       earthRadiusKm   c     i curried the function in order to be able to easily produce functions that have one of the two locations fixed and require only a pair of lat lon to produce distance

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If you need something more accurate then have a look at this      Vincenty s formulae are two related iterative methods used in geodesy   to calculate the distance between two points on the surface of a   spheroid  developed by Thaddeus Vincenty  1975a  They are based on the   assumption that the figure of the Earth is an oblate spheroid  and   hence are more accurate than methods such as great-circle distance   which assume a spherical Earth       The first  direct  method computes the location of a point which is a   given distance and azimuth  direction  from another point  The second    inverse  method computes the geographical distance and azimuth   between two given points  They have been widely used in geodesy   because they are accurate to within 0 5 mm  0 020   on the Earth   ellipsoid

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Calculate the distance between two coordinates by latitude and longitude  including a Javascript implementation   West and South locations are negative    Remember minutes and seconds are out of 60 so S31 30  is -31 50 degrees   Don t forget to convert degrees to radians   Many languages have this function   Or its a simple calculation  radians   degrees   PI   180   function degreesToRadians degrees      return degrees   Math PI   180     function distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2      var earthRadiusKm   6371     var dLat   degreesToRadians lat2-lat1     var dLon   degreesToRadians lon2-lon1      lat1   degreesToRadians lat1     lat2   degreesToRadians 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 atan2 Math sqrt a   Math sqrt 1-a       return earthRadiusKm   c      Here are some examples of usage   distanceInKmBetweenEarthCoordinates 0 0 0 0      Distance between same                                                   points should be 0 0  distanceInKmBetweenEarthCoordinates 51 5  0  38 8  -77 1     From London                                                              to Arlington 5918 185064088764

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here is the Swift implementation from the answer  func degreesToRadians degrees  Double  - gt  Double       return degrees   Double pi   180    func distanceInKmBetweenEarthCoordinates lat1  Double  lon1  Double  lat2  Double  lon2  Double  - gt  Double        let earthRadiusKm  Double   6371      let dLat   degreesToRadians degrees  lat2 - lat1      let dLon   degreesToRadians degrees  lon2 - lon1       let lat1   degreesToRadians degrees  lat1      let lat2   degreesToRadians degrees  lat2       let a   sin dLat 2    sin dLat 2        sin dLon 2    sin dLon 2    cos lat1    cos lat2      let c   2   atan2 sqrt a   sqrt 1 - a       return earthRadiusKm   c

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Dart Version  Haversine Algorithm   import  dart math    class GeoUtils      static double  degreesToRadians degrees        return degrees   pi   180         static double distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2        var earthRadiusKm   6371       var dLat    degreesToRadians lat2-lat1       var dLon    degreesToRadians lon2-lon1        lat1    degreesToRadians lat1       lat2    degreesToRadians lat2        var a   sin dLat 2    sin dLat 2            sin dLon 2    sin dLon 2    cos lat1    cos lat2       var c   2   atan2 sqrt a   sqrt 1-a        return earthRadiusKm   c

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C  Version of Haversine  double  eQuatorialEarthRadius   6378 1370D  double  d2r    Math PI   180D    private int HaversineInM double lat1  double long1  double lat2  double long2        return  int  1000D   HaversineInKM lat1  long1  lat2  long2       private double HaversineInKM double lat1  double long1  double lat2  double long2        double dlong    long2 - long1     d2r      double dlat    lat2 - lat1     d2r      double a   Math Pow Math Sin dlat   2D   2D    Math Cos lat1    d2r    Math Cos lat2    d2r    Math Pow Math Sin dlong   2D   2D       double c   2D   Math Atan2 Math Sqrt a   Math Sqrt 1D - a        double d    eQuatorialEarthRadius   c       return d      Here s a  NET Fiddle of this  so you can test it out with your own Lat Longs

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private double deg2rad double deg                return  deg   Math PI   180 0              private double rad2deg double rad                return  rad   Math PI   180 0              private double GetDistance double lat1  double lon1  double lat2  double lon2                  code for Distance in Kilo Meter         double theta   lon1 - lon2          double dist   Math Sin deg2rad lat1     Math Sin deg2rad lat2     Math Cos deg2rad lat1     Math Cos deg2rad lat2     Math Cos deg2rad theta            dist   Math Abs Math Round rad2deg Math Acos dist     60   1 1515   1 609344   1000  0            return  dist              private double GetDirection double lat1  double lon1  double lat2  double lon2                  code for Direction in Degrees         double dlat   deg2rad lat1  - deg2rad lat2           double dlon   deg2rad lon1  - deg2rad lon2           double y   Math Sin dlon    Math Cos lat2           double x   Math Cos deg2rad lat1     Math Sin deg2rad lat2   - Math Sin deg2rad lat1     Math Cos deg2rad lat2     Math Cos dlon           double direct   Math Round rad2deg Math Atan2 y  x    0           if  direct  lt  0              direct   direct   360          return  direct              private double GetSpeed double lat1  double lon1  double lat2  double lon2  DateTime CurTime  DateTime PrevTime                  code for speed in Kilo Meter Hour         TimeSpan TimeDifference   CurTime Subtract PrevTime           double TimeDifferenceInSeconds   Math Round TimeDifference TotalSeconds  0           double theta   lon1 - lon2          double dist   Math Sin deg2rad lat1     Math Sin deg2rad lat2     Math Cos deg2rad lat1     Math Cos deg2rad lat2     Math Cos deg2rad theta            dist   rad2deg Math Acos dist     60   1 1515   1 609344          double Speed   Math Abs Math Round  dist   Math Abs TimeDifferenceInSeconds     60   60  0            return  Speed              private double GetDuration DateTime CurTime  DateTime PrevTime                  code for speed in Kilo Meter Hour         TimeSpan TimeDifference   CurTime Subtract PrevTime           double TimeDifferenceInSeconds   Math Abs Math Round TimeDifference TotalSeconds  0            return  TimeDifferenceInSeconds

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Here s my implementation in Elixir  defmodule Geo do    earth radius km 6371    earth radius sm 3958 748    earth radius nm 3440 065    feet per sm 5280     d2r  math pi   180    def deg to rad deg   do  deg    d2r    def great circle distance p1  p2   km   do  haversine p1  p2     earth radius km   def great circle distance p1  p2   sm   do  haversine p1  p2     earth radius sm   def great circle distance p1  p2   nm   do  haversine p1  p2     earth radius nm   def great circle distance p1  p2   m   do  great circle distance p1  p2   km    1000   def great circle distance p1  p2   ft   do  great circle distance p1  p2   sm     feet per sm     doc       Calculate the  Haversine  https   en wikipedia org wiki Haversine formula    distance between two coordinates  Result is in radians  This result can be   multiplied by the sphere s radius in any unit to get the distance in that unit    For example  multiple the result of this function by the Earth s radius in   kilometres and you get the distance between the two given points in kilometres          def haversine  lat1  lon1    lat2  lon2   do     dlat   deg to rad lat2 - lat1      dlon   deg to rad lon2 - lon1       radlat1   deg to rad lat1      radlat2   deg to rad lat2       a    math pow  math sin dlat   2   2             math pow  math sin dlon   2   2             math cos radlat1     math cos radlat2       2    math atan2  math sqrt a    math sqrt 1 - a     end end

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Calculate the distance between two coordinates by latitude and longitude  including a Javascript implementation   West and South locations are negative    Remember minutes and seconds are out of 60 so S31 30  is -31 50 degrees   Don t forget to convert degrees to radians   Many languages have this function   Or its a simple calculation  radians   degrees   PI   180   function degreesToRadians degrees      return degrees   Math PI   180     function distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2      var earthRadiusKm   6371     var dLat   degreesToRadians lat2-lat1     var dLon   degreesToRadians lon2-lon1      lat1   degreesToRadians lat1     lat2   degreesToRadians 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 atan2 Math sqrt a   Math sqrt 1-a       return earthRadiusKm   c      Here are some examples of usage   distanceInKmBetweenEarthCoordinates 0 0 0 0      Distance between same                                                   points should be 0 0  distanceInKmBetweenEarthCoordinates 51 5  0  38 8  -77 1     From London                                                              to Arlington 5918 185064088764

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you can find a implementation of this  with some good explanation  in F  on fssnip  here are the important parts    let GreatCircleDistance lt  ltMeasure gt   u gt  R   float lt u gt   p1   Location   p2   Location        let degToRad  x   float ltdeg gt    System Math PI   x   180 0 ltdeg rad gt      let sq x   x   x        take the sin of the half and square the result     let sinSqHf  a   float ltrad gt     System Math Sin  gt gt sq   a   2 0 ltrad gt      let cos  a   float ltdeg gt    System Math Cos  degToRad a   1 0 ltrad gt       let dLat    p2 Latitude - p1 Latitude    gt degToRad     let dLon    p2 Longitude - p1 Longitude    gt degToRad      let a   sinSqHf dLat   cos p1 Latitude   cos p2 Latitude   sinSqHf dLon     let c   2 0   System Math Atan2 System Math Sqrt a   System Math Sqrt 1 0-a        R   c

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Here s a Kotlin variation   import kotlin math    class HaversineAlgorithm        companion object           private const val MEAN EARTH RADIUS   6371 0         private const val D2R   Math PI   180 0            private fun haversineInKm lat1  Double  lon1  Double  lat2  Double  lon2  Double   Double           val lonDiff    lon2 - lon1    D2R         val latDiff    lat2 - lat1    D2R         val latSin   sin latDiff   2 0          val lonSin   sin lonDiff   2 0          val a   latSin   latSin    cos lat1   D2R    cos lat2   D2R    lonSin   lonSin          val c   2 0   atan2 sqrt a   sqrt 1 0 - a           return EQATORIAL EARTH RADIUS   c

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C  Version of Haversine  double  eQuatorialEarthRadius   6378 1370D  double  d2r    Math PI   180D    private int HaversineInM double lat1  double long1  double lat2  double long2        return  int  1000D   HaversineInKM lat1  long1  lat2  long2       private double HaversineInKM double lat1  double long1  double lat2  double long2        double dlong    long2 - long1     d2r      double dlat    lat2 - lat1     d2r      double a   Math Pow Math Sin dlat   2D   2D    Math Cos lat1    d2r    Math Cos lat2    d2r    Math Pow Math Sin dlong   2D   2D       double c   2D   Math Atan2 Math Sqrt a   Math Sqrt 1D - a        double d    eQuatorialEarthRadius   c       return d      Here s a  NET Fiddle of this  so you can test it out with your own Lat Longs

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This is very easy to do with geography type in SQL Server 2008   SELECT geography  Point lat1  lon1  4326  STDistance geography  Point lat2  lon2  4326   -- computes distance in meters using eliptical model  accurate to the mm   4326 is SRID for WGS84 elipsoidal Earth model

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here is the Swift implementation from the answer  func degreesToRadians degrees  Double  - gt  Double       return degrees   Double pi   180    func distanceInKmBetweenEarthCoordinates lat1  Double  lon1  Double  lat2  Double  lon2  Double  - gt  Double        let earthRadiusKm  Double   6371      let dLat   degreesToRadians degrees  lat2 - lat1      let dLon   degreesToRadians degrees  lon2 - lon1       let lat1   degreesToRadians degrees  lat1      let lat2   degreesToRadians degrees  lat2       let a   sin dLat 2    sin dLat 2        sin dLon 2    sin dLon 2    cos lat1    cos lat2      let c   2   atan2 sqrt a   sqrt 1 - a       return earthRadiusKm   c

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PHP version    Remove all deg2rad   if your coordinates are already in radians     R   6371     km  dLat   deg2rad  lat2- lat1    dLon   deg2rad  lon2- lon1    lat1   deg2rad  lat1    lat2   deg2rad  lat2     a   sin  dLat 2    sin  dLat 2         sin  dLon 2    sin  dLon 2    cos  lat1    cos  lat2      c   2   atan2 sqrt  a   sqrt 1- a      d    R    c

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Here it is in C   lat and long in radians    double CalculateGreatCircleDistance double lat1  double long1  double lat2  double long2  double radius        return radius   Math Acos          Math Sin lat1    Math Sin lat2            Math Cos lat1    Math Cos lat2    Math Cos long2 - long1        If your lat and long are in degrees then divide by 180 PI to convert to radians

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Here s a Haversine function in Python that I use   from math import pi sqrt sin cos atan2  def haversine pos1  pos2       lat1   float pos1  lat        long1   float pos1  long        lat2   float pos2  lat        long2   float pos2  long         degree to rad   float pi   180 0       d lat    lat2 - lat1    degree to rad     d long    long2 - long1    degree to rad      a   pow sin d lat   2   2    cos lat1   degree to rad    cos lat2   degree to rad    pow sin d long   2   2      c   2   atan2 sqrt a   sqrt 1 - a       km   6367   c     mi   3956   c      return   km  km   miles  mi

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I guess you want it along the curvature of the earth  Your two points and the center of the earth are on a plane  The center of the earth is the center of a circle on that plane and the two points are  roughly  on the perimeter of that circle  From that you can calculate the distance by finding out what the angle from one point to the other is   If the points are not the same heights  or if you need to take into account that the earth is not a perfect sphere it gets a little more difficult

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It depends on how accurate you need it to be  if you need pinpoint accuracy  is best to look at an algorithm with uses an ellipsoid  rather than a sphere  such as Vincenty s algorithm  which is accurate to the mm  http   en wikipedia org wiki Vincenty 27s algorithm

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Dart Version  Haversine Algorithm   import  dart math    class GeoUtils      static double  degreesToRadians degrees        return degrees   pi   180         static double distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2        var earthRadiusKm   6371       var dLat    degreesToRadians lat2-lat1       var dLon    degreesToRadians lon2-lon1        lat1    degreesToRadians lat1       lat2    degreesToRadians lat2        var a   sin dLat 2    sin dLat 2            sin dLon 2    sin dLon 2    cos lat1    cos lat2       var c   2   atan2 sqrt a   sqrt 1-a        return earthRadiusKm   c

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I  Regarding  Breadcrumbs  method   Earth radius is different on different Lat  This must be taken into consideration in Haversine algorithm  Consider Bearing change  which turns straight lines to arches  which are longer  Taking Speed change into account will turn arches to spirals  which are longer or shorter than arches  Altitude change will turn flat spirals to 3D spirals  which are longer again   This is very important for hilly areas    Below see the function in C which takes  1 and  2 into account   double   calcDistanceByHaversine double rLat1  double rLon1  double rHeading1         double rLat2  double rLon2  double rHeading2     double rDLatRad   0 0    double rDLonRad   0 0    double rLat1Rad   0 0    double rLat2Rad   0 0    double a   0 0    double c   0 0    double rResult   0 0    double rEarthRadius   0 0    double rDHeading   0 0    double rDHeadingRad   0 0     if   rLat1  lt  -90 0      rLat1  gt  90 0      rLat2  lt  -90 0      rLat2  gt  90 0                    rLon1  lt  -180 0      rLon1  gt  180 0      rLon2  lt  -180 0                    rLon2  gt  180 0             return -1          rDLatRad    rLat2 - rLat1    DEGREE TO RADIANS    rDLonRad    rLon2 - rLon1    DEGREE TO RADIANS    rLat1Rad   rLat1   DEGREE TO RADIANS    rLat2Rad   rLat2   DEGREE TO RADIANS     a   sin rDLatRad   2    sin rDLatRad   2    sin rDLonRad   2    sin                rDLonRad   2    cos rLat1Rad    cos rLat2Rad      if  a    0 0            return 0 0         c   2   atan2 sqrt a   sqrt 1 - a      rEarthRadius   6378 1370 -  21 3847   90 0     fabs rLat1    fabs rLat2                   2 0      rResult   rEarthRadius   c        Chord to Arc Correction based on Heading changes  Important for routes with many turns and U-turns    if   rHeading1  gt   0 0   amp  amp   rHeading1  lt  360 0   amp  amp   rHeading2  gt   0 0                 amp  amp   rHeading2  lt  360 0             rDHeading   fabs rHeading1 - rHeading2           if  rDHeading  gt  180 0                  rDHeading -  180 0                    rDHeadingRad   rDHeading   DEGREE TO RADIANS          if  rDHeading  gt  5 0                  rResult   rResult    rDHeadingRad    2 0   sin rDHeadingRad   2               else                 rResult   rResult   cos rDHeadingRad                   return rResult      II  There is an easier way which gives pretty good results   By Average Speed   Trip distance   Trip average speed   Trip time  Since GPS Speed is detected by Doppler effect and is not directly related to  Lon Lat  it can be  at least considered as secondary  backup or correction  if not as main distance calculation method

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This Lua code is adapted from stuff found on Wikipedia and in Robert Lipe s GPSbabel tool   local EARTH RAD   6378137 0    -- earth s radius in meters  official geoid datum  not 20 000km   pi   local radmiles   EARTH RAD 100 0 2 54 12 0 5280 0    -- earth s radius in miles  local multipliers       radians   1  miles   radmiles  mi   radmiles  feet   radmiles   5280    meters   EARTH RAD  m   EARTH RAD  km   EARTH RAD   1000     degrees   360    2   math pi   min   60   360    2   math pi     function gcdist pt1  pt2  units  -- return distance in radians or given units   --- this formula works best for points close together or antipodal   --- rounding error strikes when distance is one-quarter Earth s circumference   ---  ref  wikipedia Great-circle distance    if not pt1 radians then pt1   rad pt1  end   if not pt2 radians then pt2   rad pt2  end   local sdlat   sin  pt1 lat - pt2 lat    2 0     local sdlon   sin  pt1 lon - pt2 lon    2 0     local res   sqrt sdlat   sdlat   cos pt1 lat    cos pt2 lat    sdlon   sdlon     res   res  gt  1 and 1 or res  lt  -1 and -1 or res   res   2   asin res     if units then return res   assert multipliers units     else return res   end end

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I guess you want it along the curvature of the earth  Your two points and the center of the earth are on a plane  The center of the earth is the center of a circle on that plane and the two points are  roughly  on the perimeter of that circle  From that you can calculate the distance by finding out what the angle from one point to the other is   If the points are not the same heights  or if you need to take into account that the earth is not a perfect sphere it gets a little more difficult

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Scala version    def deg2rad deg  Double    deg   Math PI   180 0    def rad2deg rad  Double    rad   Math PI   180 0    def getDistanceMeters lat1  Double  lon1  Double  lat2  Double  lon2  Double          val theta   lon1 - lon2     val dist   Math sin deg2rad lat1     Math sin deg2rad lat2     Math cos deg2rad lat1           Math cos deg2rad lat2     Math cos deg2rad theta       Math abs        Math round          rad2deg Math acos dist     60   1 1515   1 609344   1000

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I think a version of the algorithm in R is still missing   gpsdistance lt -function lat1 lon1 lat2 lon2      internal function to change deg to rad  degreesToRadians lt - function  degrees    return  degrees   pi   180     R lt -6371e3   radius of Earth in meters  phi1 lt -degreesToRadians lat1    latitude 1 phi2 lt -degreesToRadians lat2    latitude 2 lambda1 lt -degreesToRadians lon1    longitude 1 lambda2 lt -degreesToRadians lon2    longitude 2  delta phi lt -phi1-phi2   latitude-distance delta lambda lt -lambda1-lambda2   longitude-distance  a lt -sin delta phi 2  sin delta phi 2   cos phi1  cos phi2  sin delta lambda 2   sin delta lambda 2   cc lt -2 atan2 sqrt a  sqrt 1-a    distance lt - R   cc  return distance     in meters

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PHP version    Remove all deg2rad   if your coordinates are already in radians     R   6371     km  dLat   deg2rad  lat2- lat1    dLon   deg2rad  lon2- lon1    lat1   deg2rad  lat1    lat2   deg2rad  lat2     a   sin  dLat 2    sin  dLat 2         sin  dLon 2    sin  dLon 2    cos  lat1    cos  lat2      c   2   atan2 sqrt  a   sqrt 1- a      d    R    c

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This Lua code is adapted from stuff found on Wikipedia and in Robert Lipe s GPSbabel tool   local EARTH RAD   6378137 0    -- earth s radius in meters  official geoid datum  not 20 000km   pi   local radmiles   EARTH RAD 100 0 2 54 12 0 5280 0    -- earth s radius in miles  local multipliers       radians   1  miles   radmiles  mi   radmiles  feet   radmiles   5280    meters   EARTH RAD  m   EARTH RAD  km   EARTH RAD   1000     degrees   360    2   math pi   min   60   360    2   math pi     function gcdist pt1  pt2  units  -- return distance in radians or given units   --- this formula works best for points close together or antipodal   --- rounding error strikes when distance is one-quarter Earth s circumference   ---  ref  wikipedia Great-circle distance    if not pt1 radians then pt1   rad pt1  end   if not pt2 radians then pt2   rad pt2  end   local sdlat   sin  pt1 lat - pt2 lat    2 0     local sdlon   sin  pt1 lon - pt2 lon    2 0     local res   sqrt sdlat   sdlat   cos pt1 lat    cos pt2 lat    sdlon   sdlon     res   res  gt  1 and 1 or res  lt  -1 and -1 or res   res   2   asin res     if units then return res   assert multipliers units     else return res   end end

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Here s a Haversine function in Python that I use   from math import pi sqrt sin cos atan2  def haversine pos1  pos2       lat1   float pos1  lat        long1   float pos1  long        lat2   float pos2  lat        long2   float pos2  long         degree to rad   float pi   180 0       d lat    lat2 - lat1    degree to rad     d long    long2 - long1    degree to rad      a   pow sin d lat   2   2    cos lat1   degree to rad    cos lat2   degree to rad    pow sin d long   2   2      c   2   atan2 sqrt a   sqrt 1 - a       km   6367   c     mi   3956   c      return   km  km   miles  mi

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Java Version of Haversine Algorithm based on Roman Makarov s reply to this thread  public class HaversineAlgorithm        static final double  eQuatorialEarthRadius   6378 1370D      static final double  d2r    Math PI   180D        public static int HaversineInM double lat1  double long1  double lat2  double long2            return  int   1000D   HaversineInKM lat1  long1  lat2  long2               public static double HaversineInKM double lat1  double long1  double lat2  double long2            double dlong    long2 - long1     d2r          double dlat    lat2 - lat1     d2r          double a   Math pow Math sin dlat   2D   2D    Math cos lat1    d2r    Math cos lat2    d2r                    Math pow Math sin dlong   2D   2D           double c   2D   Math atan2 Math sqrt a   Math sqrt 1D - a            double d    eQuatorialEarthRadius   c           return d

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Here s a Kotlin variation   import kotlin math    class HaversineAlgorithm        companion object           private const val MEAN EARTH RADIUS   6371 0         private const val D2R   Math PI   180 0            private fun haversineInKm lat1  Double  lon1  Double  lat2  Double  lon2  Double   Double           val lonDiff    lon2 - lon1    D2R         val latDiff    lat2 - lat1    D2R         val latSin   sin latDiff   2 0          val lonSin   sin lonDiff   2 0          val a   latSin   latSin    cos lat1   D2R    cos lat2   D2R    lonSin   lonSin          val c   2 0   atan2 sqrt a   sqrt 1 0 - a           return EQATORIAL EARTH RADIUS   c

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Look for haversine with Google  here is my solution    include  lt math h gt   include  haversine h    define d2r  M PI   180 0     calculate haversine distance for linear distance double haversine km double lat1  double long1  double lat2  double long2        double dlong    long2 - long1    d2r      double dlat    lat2 - lat1    d2r      double a   pow sin dlat 2 0   2    cos lat1 d2r    cos lat2 d2r    pow sin dlong 2 0   2       double c   2   atan2 sqrt a   sqrt 1-a        double d   6367   c       return d     double haversine mi double lat1  double long1  double lat2  double long2        double dlong    long2 - long1    d2r      double dlat    lat2 - lat1    d2r      double a   pow sin dlat 2 0   2    cos lat1 d2r    cos lat2 d2r    pow sin dlong 2 0   2       double c   2   atan2 sqrt a   sqrt 1-a        double d   3956   c        return d

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This Lua code is adapted from stuff found on Wikipedia and in Robert Lipe s GPSbabel tool   local EARTH RAD   6378137 0    -- earth s radius in meters  official geoid datum  not 20 000km   pi   local radmiles   EARTH RAD 100 0 2 54 12 0 5280 0    -- earth s radius in miles  local multipliers       radians   1  miles   radmiles  mi   radmiles  feet   radmiles   5280    meters   EARTH RAD  m   EARTH RAD  km   EARTH RAD   1000     degrees   360    2   math pi   min   60   360    2   math pi     function gcdist pt1  pt2  units  -- return distance in radians or given units   --- this formula works best for points close together or antipodal   --- rounding error strikes when distance is one-quarter Earth s circumference   ---  ref  wikipedia Great-circle distance    if not pt1 radians then pt1   rad pt1  end   if not pt2 radians then pt2   rad pt2  end   local sdlat   sin  pt1 lat - pt2 lat    2 0     local sdlon   sin  pt1 lon - pt2 lon    2 0     local res   sqrt sdlat   sdlat   cos pt1 lat    cos pt2 lat    sdlon   sdlon     res   res  gt  1 and 1 or res  lt  -1 and -1 or res   res   2   asin res     if units then return res   assert multipliers units     else return res   end end

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I needed to implement this in PowerShell  hope it can help someone else  Some notes about this method   Don t split any of the lines or the calculation will be wrong   To calculate in KM remove the   1000 in the calculation of  distance   Change  earthsRadius   3963 19059 and remove   1000 in the calculation of  distance the to calulate the distance in miles I m using Haversine  as other posts have pointed out Vincenty s formulae is much more accurate  Function MetresDistanceBetweenTwoGPSCoordinates  latitude1   longitude1   latitude2   longitude2           Rad     math   PI   180         earthsRadius   6378 1370   Earth s Radius in KM      dLat     latitude2 -  latitude1     Rad      dLon     longitude2 -  longitude1     Rad      latitude1    latitude1    Rad      latitude2    latitude2    Rad       a    math   Sin  dLat   2     math   Sin  dLat   2     math   Sin  dLon   2     math   Sin  dLon   2     math   Cos  latitude1     math   Cos  latitude2       c   2    math   ATan2  math   Sqrt  a    math   Sqrt 1- a         distance    math   Round  earthsRadius    c   1000  0   Multiple by 1000 to get metres      Return  distance

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Here s my implementation in Elixir  defmodule Geo do    earth radius km 6371    earth radius sm 3958 748    earth radius nm 3440 065    feet per sm 5280     d2r  math pi   180    def deg to rad deg   do  deg    d2r    def great circle distance p1  p2   km   do  haversine p1  p2     earth radius km   def great circle distance p1  p2   sm   do  haversine p1  p2     earth radius sm   def great circle distance p1  p2   nm   do  haversine p1  p2     earth radius nm   def great circle distance p1  p2   m   do  great circle distance p1  p2   km    1000   def great circle distance p1  p2   ft   do  great circle distance p1  p2   sm     feet per sm     doc       Calculate the  Haversine  https   en wikipedia org wiki Haversine formula    distance between two coordinates  Result is in radians  This result can be   multiplied by the sphere s radius in any unit to get the distance in that unit    For example  multiple the result of this function by the Earth s radius in   kilometres and you get the distance between the two given points in kilometres          def haversine  lat1  lon1    lat2  lon2   do     dlat   deg to rad lat2 - lat1      dlon   deg to rad lon2 - lon1       radlat1   deg to rad lat1      radlat2   deg to rad lat2       a    math pow  math sin dlat   2   2             math pow  math sin dlon   2   2             math cos radlat1     math cos radlat2       2    math atan2  math sqrt a    math sqrt 1 - a     end end

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If you re using  NET don t reivent the wheel  See System Device Location  Credit to fnx in the comments in another answer   using System Device Location   double lat1   45 421527862548828D  double long1   -75 697189331054688D  double lat2   53 64135D  double long2   -113 59273D   GeoCoordinate geo1   new GeoCoordinate lat1  long1   GeoCoordinate geo2   new GeoCoordinate lat2  long2    double distance   geo1 GetDistanceTo geo2

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A T-SQL function  that I use to select records by distance for a center  Create Function   dbo   DistanceInMiles        fromLatitude float        fromLongitude float        toLatitude float        toLongitude float        returns float AS  BEGIN declare  distance float  select  distance   cast  3963   ACOS round COS RADIANS 90- fromLatitude   COS RADIANS 90- toLatitude     SIN RADIANS 90- fromLatitude   SIN RADIANS 90- toLatitude   COS RADIANS  fromLongitude- toLongitude   15     as float     return  round  distance 1  END

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It depends on how accurate you need it to be  if you need pinpoint accuracy  is best to look at an algorithm with uses an ellipsoid  rather than a sphere  such as Vincenty s algorithm  which is accurate to the mm  http   en wikipedia org wiki Vincenty 27s algorithm

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This is version from  Henry Vilinskiy  adapted for MySQL and Kilometers   CREATE FUNCTION  CalculateDistanceInKm     fromLatitude float    fromLongitude float    toLatitude float     toLongitude float   RETURNS float BEGIN   declare distance float     select      6367   ACOS              round                COS RADIANS 90-fromLatitude                     COS RADIANS 90-toLatitude                     SIN RADIANS 90-fromLatitude                     SIN RADIANS 90-toLatitude                     COS RADIANS fromLongitude-toLongitude                  15                    into distance     return  round distance 3   END

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A T-SQL function  that I use to select records by distance for a center  Create Function   dbo   DistanceInMiles        fromLatitude float        fromLongitude float        toLatitude float        toLongitude float        returns float AS  BEGIN declare  distance float  select  distance   cast  3963   ACOS round COS RADIANS 90- fromLatitude   COS RADIANS 90- toLatitude     SIN RADIANS 90- fromLatitude   SIN RADIANS 90- toLatitude   COS RADIANS  fromLongitude- toLongitude   15     as float     return  round  distance 1  END

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Here it is in C   lat and long in radians    double CalculateGreatCircleDistance double lat1  double long1  double lat2  double long2  double radius        return radius   Math Acos          Math Sin lat1    Math Sin lat2            Math Cos lat1    Math Cos lat2    Math Cos long2 - long1        If your lat and long are in degrees then divide by 180 PI to convert to radians

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Calculate the distance between two coordinates by latitude and longitude  including a Javascript implementation   West and South locations are negative    Remember minutes and seconds are out of 60 so S31 30  is -31 50 degrees   Don t forget to convert degrees to radians   Many languages have this function   Or its a simple calculation  radians   degrees   PI   180   function degreesToRadians degrees      return degrees   Math PI   180     function distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2      var earthRadiusKm   6371     var dLat   degreesToRadians lat2-lat1     var dLon   degreesToRadians lon2-lon1      lat1   degreesToRadians lat1     lat2   degreesToRadians 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 atan2 Math sqrt a   Math sqrt 1-a       return earthRadiusKm   c      Here are some examples of usage   distanceInKmBetweenEarthCoordinates 0 0 0 0      Distance between same                                                   points should be 0 0  distanceInKmBetweenEarthCoordinates 51 5  0  38 8  -77 1     From London                                                              to Arlington 5918 185064088764

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If you re using  NET don t reivent the wheel  See System Device Location  Credit to fnx in the comments in another answer   using System Device Location   double lat1   45 421527862548828D  double long1   -75 697189331054688D  double lat2   53 64135D  double long2   -113 59273D   GeoCoordinate geo1   new GeoCoordinate lat1  long1   GeoCoordinate geo2   new GeoCoordinate lat2  long2    double distance   geo1 GetDistanceTo geo2

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If you need something more accurate then have a look at this      Vincenty s formulae are two related iterative methods used in geodesy   to calculate the distance between two points on the surface of a   spheroid  developed by Thaddeus Vincenty  1975a  They are based on the   assumption that the figure of the Earth is an oblate spheroid  and   hence are more accurate than methods such as great-circle distance   which assume a spherical Earth       The first  direct  method computes the location of a point which is a   given distance and azimuth  direction  from another point  The second    inverse  method computes the geographical distance and azimuth   between two given points  They have been widely used in geodesy   because they are accurate to within 0 5 mm  0 020   on the Earth   ellipsoid

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I think a version of the algorithm in R is still missing   gpsdistance lt -function lat1 lon1 lat2 lon2      internal function to change deg to rad  degreesToRadians lt - function  degrees    return  degrees   pi   180     R lt -6371e3   radius of Earth in meters  phi1 lt -degreesToRadians lat1    latitude 1 phi2 lt -degreesToRadians lat2    latitude 2 lambda1 lt -degreesToRadians lon1    longitude 1 lambda2 lt -degreesToRadians lon2    longitude 2  delta phi lt -phi1-phi2   latitude-distance delta lambda lt -lambda1-lambda2   longitude-distance  a lt -sin delta phi 2  sin delta phi 2   cos phi1  cos phi2  sin delta lambda 2   sin delta lambda 2   cc lt -2 atan2 sqrt a  sqrt 1-a    distance lt - R   cc  return distance     in meters

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It depends on how accurate you need it to be  if you need pinpoint accuracy  is best to look at an algorithm with uses an ellipsoid  rather than a sphere  such as Vincenty s algorithm  which is accurate to the mm  http   en wikipedia org wiki Vincenty 27s algorithm

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This is very easy to do with geography type in SQL Server 2008   SELECT geography  Point lat1  lon1  4326  STDistance geography  Point lat2  lon2  4326   -- computes distance in meters using eliptical model  accurate to the mm   4326 is SRID for WGS84 elipsoidal Earth model

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i took the top answer and used it in a Scala program  import java lang Math  atan2  cos  sin  sqrt   def latLonDistance lat1  Double  lon1  Double  lat2  Double  lon2  Double   Double         val earthRadiusKm   6371     val dLat    lat2 - lat1  toRadians     val dLon    lon2 - lon1  toRadians     val latRad1   lat1 toRadians     val latRad2   lat2 toRadians      val a   sin dLat   2    sin dLat   2    sin dLon   2    sin dLon   2    cos latRad1    cos latRad2      val c   2   atan2 sqrt a   sqrt 1 - a       earthRadiusKm   c     i curried the function in order to be able to easily produce functions that have one of the two locations fixed and require only a pair of lat lon to produce distance

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Calculate the distance between two coordinates by latitude and longitude  including a Javascript implementation   West and South locations are negative    Remember minutes and seconds are out of 60 so S31 30  is -31 50 degrees   Don t forget to convert degrees to radians   Many languages have this function   Or its a simple calculation  radians   degrees   PI   180   function degreesToRadians degrees      return degrees   Math PI   180     function distanceInKmBetweenEarthCoordinates lat1  lon1  lat2  lon2      var earthRadiusKm   6371     var dLat   degreesToRadians lat2-lat1     var dLon   degreesToRadians lon2-lon1      lat1   degreesToRadians lat1     lat2   degreesToRadians 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 atan2 Math sqrt a   Math sqrt 1-a       return earthRadiusKm   c      Here are some examples of usage   distanceInKmBetweenEarthCoordinates 0 0 0 0      Distance between same                                                   points should be 0 0  distanceInKmBetweenEarthCoordinates 51 5  0  38 8  -77 1     From London                                                              to Arlington 5918 185064088764

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I guess you want it along the curvature of the earth  Your two points and the center of the earth are on a plane  The center of the earth is the center of a circle on that plane and the two points are  roughly  on the perimeter of that circle  From that you can calculate the distance by finding out what the angle from one point to the other is   If the points are not the same heights  or if you need to take into account that the earth is not a perfect sphere it gets a little more difficult

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This is version from  Henry Vilinskiy  adapted for MySQL and Kilometers   CREATE FUNCTION  CalculateDistanceInKm     fromLatitude float    fromLongitude float    toLatitude float     toLongitude float   RETURNS float BEGIN   declare distance float     select      6367   ACOS              round                COS RADIANS 90-fromLatitude                     COS RADIANS 90-toLatitude                     SIN RADIANS 90-fromLatitude                     SIN RADIANS 90-toLatitude                     COS RADIANS fromLongitude-toLongitude                  15                    into distance     return  round distance 3   END

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This Lua code is adapted from stuff found on Wikipedia and in Robert Lipe s GPSbabel tool   local EARTH RAD   6378137 0    -- earth s radius in meters  official geoid datum  not 20 000km   pi   local radmiles   EARTH RAD 100 0 2 54 12 0 5280 0    -- earth s radius in miles  local multipliers       radians   1  miles   radmiles  mi   radmiles  feet   radmiles   5280    meters   EARTH RAD  m   EARTH RAD  km   EARTH RAD   1000     degrees   360    2   math pi   min   60   360    2   math pi     function gcdist pt1  pt2  units  -- return distance in radians or given units   --- this formula works best for points close together or antipodal   --- rounding error strikes when distance is one-quarter Earth s circumference   ---  ref  wikipedia Great-circle distance    if not pt1 radians then pt1   rad pt1  end   if not pt2 radians then pt2   rad pt2  end   local sdlat   sin  pt1 lat - pt2 lat    2 0     local sdlon   sin  pt1 lon - pt2 lon    2 0     local res   sqrt sdlat   sdlat   cos pt1 lat    cos pt2 lat    sdlon   sdlon     res   res  gt  1 and 1 or res  lt  -1 and -1 or res   res   2   asin res     if units then return res   assert multipliers units     else return res   end end

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I needed to implement this in PowerShell  hope it can help someone else  Some notes about this method   Don t split any of the lines or the calculation will be wrong   To calculate in KM remove the   1000 in the calculation of  distance   Change  earthsRadius   3963 19059 and remove   1000 in the calculation of  distance the to calulate the distance in miles I m using Haversine  as other posts have pointed out Vincenty s formulae is much more accurate  Function MetresDistanceBetweenTwoGPSCoordinates  latitude1   longitude1   latitude2   longitude2           Rad     math   PI   180         earthsRadius   6378 1370   Earth s Radius in KM      dLat     latitude2 -  latitude1     Rad      dLon     longitude2 -  longitude1     Rad      latitude1    latitude1    Rad      latitude2    latitude2    Rad       a    math   Sin  dLat   2     math   Sin  dLat   2     math   Sin  dLon   2     math   Sin  dLon   2     math   Cos  latitude1     math   Cos  latitude2       c   2    math   ATan2  math   Sqrt  a    math   Sqrt 1- a         distance    math   Round  earthsRadius    c   1000  0   Multiple by 1000 to get metres      Return  distance

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Scala version    def deg2rad deg  Double    deg   Math PI   180 0    def rad2deg rad  Double    rad   Math PI   180 0    def getDistanceMeters lat1  Double  lon1  Double  lat2  Double  lon2  Double          val theta   lon1 - lon2     val dist   Math sin deg2rad lat1     Math sin deg2rad lat2     Math cos deg2rad lat1           Math cos deg2rad lat2     Math cos deg2rad theta       Math abs        Math round          rad2deg Math acos dist     60   1 1515   1 609344   1000

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It depends on how accurate you need it to be  if you need pinpoint accuracy  is best to look at an algorithm with uses an ellipsoid  rather than a sphere  such as Vincenty s algorithm  which is accurate to the mm  http   en wikipedia org wiki Vincenty 27s algorithm

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Java Version of Haversine Algorithm based on Roman Makarov s reply to this thread  public class HaversineAlgorithm        static final double  eQuatorialEarthRadius   6378 1370D      static final double  d2r    Math PI   180D        public static int HaversineInM double lat1  double long1  double lat2  double long2            return  int   1000D   HaversineInKM lat1  long1  lat2  long2               public static double HaversineInKM double lat1  double long1  double lat2  double long2            double dlong    long2 - long1     d2r          double dlat    lat2 - lat1     d2r          double a   Math pow Math sin dlat   2D   2D    Math cos lat1    d2r    Math cos lat2    d2r                    Math pow Math sin dlong   2D   2D           double c   2D   Math atan2 Math sqrt a   Math sqrt 1D - a            double d    eQuatorialEarthRadius   c           return d

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private double deg2rad double deg                return  deg   Math PI   180 0              private double rad2deg double rad                return  rad   Math PI   180 0              private double GetDistance double lat1  double lon1  double lat2  double lon2                  code for Distance in Kilo Meter         double theta   lon1 - lon2          double dist   Math Sin deg2rad lat1     Math Sin deg2rad lat2     Math Cos deg2rad lat1     Math Cos deg2rad lat2     Math Cos deg2rad theta            dist   Math Abs Math Round rad2deg Math Acos dist     60   1 1515   1 609344   1000  0            return  dist              private double GetDirection double lat1  double lon1  double lat2  double lon2                  code for Direction in Degrees         double dlat   deg2rad lat1  - deg2rad lat2           double dlon   deg2rad lon1  - deg2rad lon2           double y   Math Sin dlon    Math Cos lat2           double x   Math Cos deg2rad lat1     Math Sin deg2rad lat2   - Math Sin deg2rad lat1     Math Cos deg2rad lat2     Math Cos dlon           double direct   Math Round rad2deg Math Atan2 y  x    0           if  direct  lt  0              direct   direct   360          return  direct              private double GetSpeed double lat1  double lon1  double lat2  double lon2  DateTime CurTime  DateTime PrevTime                  code for speed in Kilo Meter Hour         TimeSpan TimeDifference   CurTime Subtract PrevTime           double TimeDifferenceInSeconds   Math Round TimeDifference TotalSeconds  0           double theta   lon1 - lon2          double dist   Math Sin deg2rad lat1     Math Sin deg2rad lat2     Math Cos deg2rad lat1     Math Cos deg2rad lat2     Math Cos deg2rad theta            dist   rad2deg Math Acos dist     60   1 1515   1 609344          double Speed   Math Abs Math Round  dist   Math Abs TimeDifferenceInSeconds     60   60  0            return  Speed              private double GetDuration DateTime CurTime  DateTime PrevTime                  code for speed in Kilo Meter Hour         TimeSpan TimeDifference   CurTime Subtract PrevTime           double TimeDifferenceInSeconds   Math Abs Math Round TimeDifference TotalSeconds  0            return  TimeDifferenceInSeconds

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I  Regarding  Breadcrumbs  method   Earth radius is different on different Lat  This must be taken into consideration in Haversine algorithm  Consider Bearing change  which turns straight lines to arches  which are longer  Taking Speed change into account will turn arches to spirals  which are longer or shorter than arches  Altitude change will turn flat spirals to 3D spirals  which are longer again   This is very important for hilly areas    Below see the function in C which takes  1 and  2 into account   double   calcDistanceByHaversine double rLat1  double rLon1  double rHeading1         double rLat2  double rLon2  double rHeading2     double rDLatRad   0 0    double rDLonRad   0 0    double rLat1Rad   0 0    double rLat2Rad   0 0    double a   0 0    double c   0 0    double rResult   0 0    double rEarthRadius   0 0    double rDHeading   0 0    double rDHeadingRad   0 0     if   rLat1  lt  -90 0      rLat1  gt  90 0      rLat2  lt  -90 0      rLat2  gt  90 0                    rLon1  lt  -180 0      rLon1  gt  180 0      rLon2  lt  -180 0                    rLon2  gt  180 0             return -1          rDLatRad    rLat2 - rLat1    DEGREE TO RADIANS    rDLonRad    rLon2 - rLon1    DEGREE TO RADIANS    rLat1Rad   rLat1   DEGREE TO RADIANS    rLat2Rad   rLat2   DEGREE TO RADIANS     a   sin rDLatRad   2    sin rDLatRad   2    sin rDLonRad   2    sin                rDLonRad   2    cos rLat1Rad    cos rLat2Rad      if  a    0 0            return 0 0         c   2   atan2 sqrt a   sqrt 1 - a      rEarthRadius   6378 1370 -  21 3847   90 0     fabs rLat1    fabs rLat2                   2 0      rResult   rEarthRadius   c        Chord to Arc Correction based on Heading changes  Important for routes with many turns and U-turns    if   rHeading1  gt   0 0   amp  amp   rHeading1  lt  360 0   amp  amp   rHeading2  gt   0 0                 amp  amp   rHeading2  lt  360 0             rDHeading   fabs rHeading1 - rHeading2           if  rDHeading  gt  180 0                  rDHeading -  180 0                    rDHeadingRad   rDHeading   DEGREE TO RADIANS          if  rDHeading  gt  5 0                  rResult   rResult    rDHeadingRad    2 0   sin rDHeadingRad   2               else                 rResult   rResult   cos rDHeadingRad                   return rResult      II  There is an easier way which gives pretty good results   By Average Speed   Trip distance   Trip average speed   Trip time  Since GPS Speed is detected by Doppler effect and is not directly related to  Lon Lat  it can be  at least considered as secondary  backup or correction  if not as main distance calculation method

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I needed to calculate a lot of distances between the points for my project  so I went ahead and tried to optimize the code  I have found here  On average in different browsers my new implementation runs 2 times faster than the most upvoted answer   function distance lat1  lon1  lat2  lon2      var p   0 017453292519943295        Math PI   180   var c   Math cos    var a   0 5 - c  lat2 - lat1    p  2              c lat1   p    c lat2   p                1 - c  lon2 - lon1    p   2     return 12742   Math asin Math sqrt a       2   R  R   6371 km     You can play with my jsPerf and see the results here   Recently I needed to do the same in python  so here is a python implementation   from math import cos  asin  sqrt def distance lat1  lon1  lat2  lon2       p   0 017453292519943295     a   0 5 - cos  lat2 - lat1    p  2   cos lat1   p    cos lat2   p     1 - cos  lon2 - lon1    p     2     return 12742   asin sqrt a     And for the sake of completeness  Haversine on wiki

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I needed to calculate a lot of distances between the points for my project  so I went ahead and tried to optimize the code  I have found here  On average in different browsers my new implementation runs 2 times faster than the most upvoted answer   function distance lat1  lon1  lat2  lon2      var p   0 017453292519943295        Math PI   180   var c   Math cos    var a   0 5 - c  lat2 - lat1    p  2              c lat1   p    c lat2   p                1 - c  lon2 - lon1    p   2     return 12742   Math asin Math sqrt a       2   R  R   6371 km     You can play with my jsPerf and see the results here   Recently I needed to do the same in python  so here is a python implementation   from math import cos  asin  sqrt def distance lat1  lon1  lat2  lon2       p   0 017453292519943295     a   0 5 - cos  lat2 - lat1    p  2   cos lat1   p    cos lat2   p     1 - cos  lon2 - lon1    p     2     return 12742   asin sqrt a     And for the sake of completeness  Haversine on wiki

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This is very easy to do with geography type in SQL Server 2008   SELECT geography  Point lat1  lon1  4326  STDistance geography  Point lat2  lon2  4326   -- computes distance in meters using eliptical model  accurate to the mm   4326 is SRID for WGS84 elipsoidal Earth model

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Maybe a typo error   We have an unused variable dlon in GetDirection  I assume   double y   Math Sin dlon    Math Cos lat2      cannot use degrees in Cos     should be   double y   Math Sin dlon    Math Cos dlat

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I guess you want it along the curvature of the earth  Your two points and the center of the earth are on a plane  The center of the earth is the center of a circle on that plane and the two points are  roughly  on the perimeter of that circle  From that you can calculate the distance by finding out what the angle from one point to the other is   If the points are not the same heights  or if you need to take into account that the earth is not a perfect sphere it gets a little more difficult

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Look for haversine with Google  here is my solution    include  lt math h gt   include  haversine h    define d2r  M PI   180 0     calculate haversine distance for linear distance double haversine km double lat1  double long1  double lat2  double long2        double dlong    long2 - long1    d2r      double dlat    lat2 - lat1    d2r      double a   pow sin dlat 2 0   2    cos lat1 d2r    cos lat2 d2r    pow sin dlong 2 0   2       double c   2   atan2 sqrt a   sqrt 1-a        double d   6367   c       return d     double haversine mi double lat1  double long1  double lat2  double long2        double dlong    long2 - long1    d2r      double dlat    lat2 - lat1    d2r      double a   pow sin dlat 2 0   2    cos lat1 d2r    cos lat2 d2r    pow sin dlong 2 0   2       double c   2   atan2 sqrt a   sqrt 1-a        double d   3956   c        return d

[math] Calculate distance between 2 GPS coordinates

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