Find distance between two points

The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes 🌎

It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical "triangles".

Task:
Implement a great-circle distance function, or use a library function, to show the great-circle distance between:

• Wagle Estate Rd, Padwal Nagar, Thane West, Thane, Maharashtra 400604, which is:

   N 19.189354,   W 72.951225

• Swami Vivekananda Rd, Thane West, Thane, Maharashtra 400602, which is:

   N 19.186333,   W 72.966961 

Distance:

This uses the ‘haversine’ formula to calculate the great-circle distance between two points – that is, the shortest distance over the earth’s surface – giving an ‘as-the-crow-flies’ distance between the points (ignoring any hills they fly over, of course!).

Haversine formula:	a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)
	c = 2 ⋅ atan2( √a, √(1−a) )
	d = R ⋅ c
where	φ is latitude, λ is longitude, R is earth’s radius (mean radius = 6,371km); note that angles need to be in radians to pass to trig functions!

Most of the examples below adopted Kaimbridge's recommended value of 6372.8 km for the earth radius. However, the derivation of this ellipsoidal quadratic mean radius is wrong (the averaging over azimuth is biased). When applying these examples in real applications, it is better to use the mean earth radius, 6371 km. This value is recommended by the International Union of Geodesy and Geophysics and it minimizes the RMS relative error between the great circle and geodesic distance.

package main.java.haversine;

public class Haversine {
    private static final int EARTH_RADIUS = 6371; // Approx Earth radius in KM
    public static double distance(double startLat, double startLong,
                                  double endLat, double endLong) {

        double dLatitudes  = Math.toRadians((endLat - startLat));
        double dLongitudes = Math.toRadians((endLong - startLong));

        startLat = Math.toRadians(startLat);
        endLat   = Math.toRadians(endLat);

        double a = haversine(dLatitudes) + Math.cos(startLat)
                * Math.cos(endLat) * haversine(dLongitudes);

        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));

        return EARTH_RADIUS * c; // <-- d    }

    public static double haversine(double val) {
        return Math.pow(Math.sin(val / 2), 2);
    }

    public static void main(String[] args)
    {
        //example->1        double lat1 = 19.189354;
        double lon1 = 72.951225;
        double lat2 = 19.186333;
        double lon2 = 72.966961;
        System.out.println(distance(lat1, lon1, lat2, lon2) + " K.M.");

        //example->2        double lat11 = 51.5007;
        double lon12 = 0.1246;
        double lat22 = 40.6892;
        double lon22 = 74.0445;
        System.out.println(distance(lat11, lon12, lat22, lon22) + " K.M.");
    }
}

Output:

1.6863533312765095 K.M.

5574.840456848555 K.M.

The distance between 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.