Calculating distance between two points using latitude longitude

Question

Here s my try  it s just a snippet of my code   final double RADIUS   6371 01  double temp   Math cos Math toRadians latA                 Math cos Math toRadians latB                 Math cos Math toRadians  latB  -  latA                  Math sin Math toRadians latA                 Math sin Math toRadians latB        return temp   RADIUS   Math PI   180    I am using this formulae to get the latitude and longitude   x   Deg    Min   Sec   60    60

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Here is a page with javascript examples for various spherical calculations. The very first one on the page should give you what you need.

http://www.movable-type.co.uk/scripts/latlong.html

Here is the Javascript code

var R = 6371; // km
var dLat = (lat2-lat1).toRad();
var dLon = (lon2-lon1).toRad(); 
var a = Math.sin(dLat/2) * Math.sin(dLat/2) + 
        Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) *
        Math.sin(dLon/2) * Math.sin(dLon/2); 
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
var d = R * c;

Where 'd' will hold the distance.

User · Answer

This wikipedia article provides the formulae and an example  The text is in german  but the calculations speak for themselves

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Here s a Java function that calculates the distance between two lat long points  posted below  just in case it disappears again      private double distance double lat1  double lon1  double lat2  double lon2  char unit          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 acos dist         dist   rad2deg dist         dist   dist   60   1 1515        if  unit     K             dist   dist   1 609344          else if  unit     N             dist   dist   0 8684                  return  dist                                                                                                    This function converts decimal degrees to radians                                                                                                 private double deg2rad double deg          return  deg   Math PI   180 0                                                                                                    This function converts radians to decimal degrees                                                                                                 private double rad2deg double rad          return  rad   180 0   Math PI                  System out println distance 32 9697  -96 80322  29 46786  -98 53506   M      quot  Miles n quot        System out println distance 32 9697  -96 80322  29 46786  -98 53506   K      quot  Kilometers n quot        System out println distance 32 9697  -96 80322  29 46786  -98 53506   N      quot  Nautical Miles n quot

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package distanceAlgorithm   public class CalDistance       public static void main String   args               TODO Auto-generated method stub     CalDistance obj new CalDistance          obj distance 38 898556  -77 037852  38 897147  -77 043934             System out println obj distance 38 898556  -77 037852  38 897147  -77 043934   M       Miles n            System out println obj distance 38 898556  -77 037852  38 897147  -77 043934   K       Kilometers n            System out println obj distance 32 9697  -96 80322  29 46786  -98 53506   N       Nautical Miles n                        public double distance double lat1  double lon1  double lat2  double lon2  String sr                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 acos dist             dist   rad2deg dist             dist   dist   60   1 1515            if  sr equals  K                  dist   dist   1 609344              else if  sr equals  N                  dist   dist   0 8684                          return  dist                 public double deg2rad double deg              return  deg   Math PI   180 0                 public double rad2deg double rad              return  rad   180 0   Math PI

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Future readers who stumble upon this SOF article   Obviously  the question was asked in 2010 and its now 2019  But it comes up early in an internet search   The original question does not discount use of third-party-library  when I wrote this answer    public double calculateDistanceInMeters double lat1  double long1  double lat2                                       double long2          double dist   org apache lucene util SloppyMath haversinMeters lat1  long1  lat2  long2       return dist      and   lt dependency gt     lt groupId gt org apache lucene lt  groupId gt     lt artifactId gt lucene-spatial lt  artifactId gt     lt version gt 8 2 0 lt  version gt   lt  dependency gt    https   mvnrepository com artifact org apache lucene lucene-spatial 8 2 0  Please read documentation about  SloppyMath  before diving in   https   lucene apache org core 8 2 0 core org apache lucene util SloppyMath html

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was a lot of great answers provided however I found some performance shortcomings  so let me offer a version with performance in mind  Every constant is precalculated and x y variables are introduced to avoid calculating the same value twice  Hope it helps     private static final double r2d   180 0D   3 141592653589793D      private static final double d2r   3 141592653589793D   180 0D      private static final double d2km   111189 57696D   r2d      public static double meters double lt1  double ln1  double lt2  double ln2            double x   lt1   d2r          double y   lt2   d2r          return Math acos  Math sin x    Math sin y    Math cos x    Math cos y    Math cos d2r    ln1 - ln2      d2km

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The Java code given by Dommer above gives slightly incorrect results but the small errors add up if you are processing say a GPS track  Here is an implementation of the Haversine method in Java which also takes into account height differences between two points          Calculate distance between two points in latitude and longitude taking    into account height difference  If you are not interested in height    difference pass 0 0  Uses Haversine method as its base         lat1  lon1 Start point lat2  lon2 End point el1 Start altitude in meters    el2 End altitude in meters     returns Distance in Meters     public static double distance double lat1  double lat2  double lon1          double lon2  double el1  double el2         final int R   6371     Radius of the earth      double latDistance   Math toRadians lat2 - lat1       double lonDistance   Math toRadians lon2 - lon1       double a   Math sin latDistance   2    Math sin latDistance   2                Math cos Math toRadians lat1     Math cos Math toRadians lat2                 Math sin lonDistance   2    Math sin lonDistance   2       double c   2   Math atan2 Math sqrt a   Math sqrt 1 - a        double distance   R   c   1000     convert to meters      double height   el1 - el2       distance   Math pow distance  2    Math pow height  2        return Math sqrt distance

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Slightly upgraded answer from  David George  public static double distance double lat1  double lat2  double lon1                                double lon2  double el1  double el2         final int R   6371     Radius of the earth      double latDistance   Math toRadians lat2 - lat1       double lonDistance   Math toRadians lon2 - lon1       double a   Math sin latDistance   2    Math sin latDistance   2                Math cos Math toRadians lat1     Math cos Math toRadians lat2                 Math sin lonDistance   2    Math sin lonDistance   2       double c   2   Math atan2 Math sqrt a   Math sqrt 1 - a        double distance   R   c   1000     convert to meters      double height   el1 - el2       distance   Math pow distance  2    Math pow height  2        return Math sqrt distance      public static double distanceBetweenLocations Location l1  Location l2        if l1 hasAltitude    amp  amp  l2 hasAltitude              return distance l1 getLatitude    l2 getLatitude    l1 getLongitude    l2 getLongitude    l1 getAltitude    l2 getAltitude               return l1 distanceTo l2      distance function is the same  but I ve created I small wrapper function  which takes 2 Location objects  Thanks to this  I only use distance function if both of locations actually have altitude  because sometimes they don t  And it can lead to strange results  if location doesn t know its altitude 0 will be returned   In this case  I fall back to classic distanceTo function

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Note  this solution only works for short distances   I tried to use dommer s posted formula for an application and found it did well for long distances but in my data I was using all very short distances  and dommer s post did very poorly  I needed speed  and the more complex geo calcs worked well but were too slow   So  in the case that you need speed and all the calculations you re making are short  maybe  lt  100m or so    I found this little approximation to work great   it assumes the world is flat mind you  so don t use it for long distances  it works by approximating the distance of a single Latitude and Longitude at the given Latitude and returning the Pythagorean distance in meters    public class FlatEarthDist         returns distance in meters     public static double distance double lat1  double lng1                                         double lat2  double lng2        double a    lat1-lat2  FlatEarthDist distPerLat lat1        double b    lng1-lng2  FlatEarthDist distPerLng lat1        return Math sqrt a a b b              private static double distPerLng double lat         return 0 0003121092 Math pow lat  4                0 0101182384 Math pow lat  3                   -17 2385140059 lat lat               5 5485277537 lat 111301 967182595             private static double distPerLat double lat               return -0 000000487305676 Math pow lat  4                  -0 0033668574 Math pow lat  3                   0 4601181791 lat lat                 -1 4558127346 lat 110579 25662316

[java] Calculating distance between two points, using latitude longitude?

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