Haversine formula to find distance between two points on a sphere
The Haversine formula calculates the shortest distance between two points on a sphere using their latitudes and longitudes measured along the surface. It is important for use in navigation. The haversine can be expressed in trignometric function as:
The haversine of the central angle (which is d/r) is calculated by the following formula:
where r is the radius of earth(6371 km), d is the distance between two points, 
is latitude of the two points and 
is longitude of the two points respectively.
Solving d by applying the inverse haversine or by using the inverse sine function, we get:
or
The distance between Big Ben in London (51.5007° N, 0.1246° W) and The Statue of Liberty in
New York (40.6892° N, 74.0445° W) is 5574.8 km. This is not the exact measurement because the
formula assumes that the Earth is a perfect sphere when in fact it is an oblate spheroid.
Below is the implementation of the above formulae:
C++
// C++ program for the haversine formula // C++ program for the // haversine formula #include <iostream> #include <cmath> using namespace std; static double haversine(double lat1, double lon1, double lat2, double lon2) { // distance between latitudes // and longitudes double dLat = (lat2 - lat1) * M_PI / 180.0; double dLon = (lon2 - lon1) * M_PI / 180.0; // convert to radians lat1 = (lat1) * M_PI / 180.0; lat2 = (lat2) * M_PI / 180.0; // apply formulae double a = pow(sin(dLat / 2), 2) + pow(sin(dLon / 2), 2) * cos(lat1) * cos(lat2); double rad = 6371; double c = 2 * asin(sqrt(a)); return rad * c; } // Driver code int main() { double lat1 = 51.5007; double lon1 = 0.1246; double lat2 = 40.6892; double lon2 = 74.0445; cout << haversine(lat1, lon1, lat2, lon2) << " K.M."; return 0; } // This code is contributed // by Mahadev. |
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Java
// Java program for the haversine formula public class Haversine { static double haversine(double lat1, double lon1, double lat2, double lon2) { // distance between latitudes and longitudes double dLat = Math.toRadians(lat2 - lat1); double dLon = Math.toRadians(lon2 - lon1); // convert to radians lat1 = Math.toRadians(lat1); lat2 = Math.toRadians(lat2); // apply formulae double a = Math.pow(Math.sin(dLat / 2), 2) + Math.pow(Math.sin(dLon / 2), 2) * Math.cos(lat1) * Math.cos(lat2); double rad = 6371; double c = 2 * Math.asin(Math.sqrt(a)); return rad * c; } // Driver Code public static void main(String[] args) { double lat1 = 51.5007; double lon1 = 0.1246; double lat2 = 40.6892; double lon2 = 74.0445; System.out.println(haversine(lat1, lon1, lat2, lon2) + " K.M."); } } |
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Python 3
# Python 3 program for the # haversine formula import math # Python 3 program for the # haversine formula def haversine(lat1, lon1, lat2, lon2): # distance between latitudes # and longitudes dLat = (lat2 - lat1) * math.pi / 180.0 dLon = (lon2 - lon1) * math.pi / 180.0 # convert to radians lat1 = (lat1) * math.pi / 180.0 lat2 = (lat2) * math.pi / 180.0 # apply formulae a = (pow(math.sin(dLat / 2), 2) + pow(math.sin(dLon / 2), 2) * math.cos(lat1) * math.cos(lat2)); rad = 6371 c = 2 * math.asin(math.sqrt(a)) return rad * c # Driver code if __name__ == "__main__": lat1 = 51.5007 lon1 = 0.1246 lat2 = 40.6892 lon2 = 74.0445 print(haversine(lat1, lon1,lat2, lon2), "K.M.") # This code is contributed # by ChitraNayal |
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C#
// C# program for the haversine formula using System; class GFG { static double haversine(double lat1, double lon1, double lat2, double lon2) { // distance between latitudes and longitudes double dLat = (Math.PI / 180) * (lat2 - lat1); double dLon = (Math.PI / 180) * (lon2 - lon1); // convert to radians lat1 = (Math.PI / 180) * (lat1); lat2 = (Math.PI / 180) * (lat2); // apply formulae double a = Math.Pow(Math.Sin(dLat / 2), 2) + Math.Pow(Math.Sin(dLon / 2), 2) * Math.Cos(lat1) * Math.Cos(lat2); double rad = 6371; double c = 2 * Math.Asin(Math.Sqrt(a)); return rad * c; } // Driver Code public static void Main() { double lat1 = 51.5007; double lon1 = 0.1246; double lat2 = 40.6892; double lon2 = 74.0445; Console.WriteLine(haversine(lat1, lon1, lat2, lon2) + " K.M."); } } // This code is contributed // by Akanksha Rai(Abby_akku) |
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PHP
<?php // PHP program for the // haversine formula function haversine($lat1, $lon1, $lat2, $lon2) { // distance between latitudes // and longitudes $dLat = ($lat2 - $lat1) * M_PI / 180.0; $dLon = ($lon2 - $lon1) * M_PI / 180.0; // convert to radians $lat1 = ($lat1) * M_PI / 180.0; $lat2 = ($lat2) * M_PI / 180.0; // apply formulae $a = pow(sin($dLat / 2), 2) + pow(sin($dLon / 2), 2) * cos($lat1) * cos($lat2); $rad = 6371; $c = 2 * asin(sqrt($a)); return $rad * $c; } // Driver code $lat1 = 51.5007; $lon1 = 0.1246; $lat2 = 40.6892; $lon2 = 74.0445; echo haversine($lat1, $lon1, $lat2, $lon2) . " K.M."; // This code is contributed // by Akanksha Rai(Abby_akku) ?> |
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Output:
5574.840456848555 K.M.
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