How to Calculate Distance between addresses Latitude/Longitude Geo Coordinates

The EASY way is to have .NET 4 Framework or above and reference System.Device.dll, and using namespace found in System.Device.Location. (You should see it if you are developing a Windows Phone program) There is a method called GetDistanceTo().

Here is a quick example:

var location1 = new GeoCoordinates(-29.83245, 31.04034);
var location2 = new GeoCoordinates(-51.39792, -0.12084);
double distance = location1 .GetDistanceTo(location2);

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Please note that the method returns in km (kilometer).

Under the hood
The formulas used in the method is actually using the Haversine method. It assumes that the earth is a perfect sphere rather than an ellipsoid, so as a result, it has an error of less than 0.1 percent.  
Since it didn't account for altitude in its calculation, the distance is shorter than the driving distance.

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Here is the LONG way:

    public class GeoCoordinate
    {
        public double Latitude { get; set; }
        public double Longitude { get; set; }
    }

    public class GeoCoordinateTool
    {
        public double Distance(GeoCoordinate loc1, GeoCoordinate loc2, int type)
        {
            //1- miles, other km
            //Use 3960 if you want miles; use 6371 if you want km
            double R = (type == 1) ? 3960 : 6371;          // R is earth radius.
            double dLat = this.toRadian(loc2.Latitude - loc1.Latitude);
            double dLon = this.toRadian(loc2.Longitude - loc1.Longitude);

            double a = Math.Sin(dLat / 2) * Math.Sin(dLat / 2) + Math.Cos(this.toRadian(loc1.Latitude)) * Math.Cos(this.toRadian(loc2.Latitude)) * Math.Sin(dLon / 2) * Math.Sin(dLon / 2);

            double c = 2 * Math.Asin(Math.Min(1, Math.Sqrt(a)));
            double d = R * c;

            return d;
        }

        private double toRadian(double val)
        {
            return (Math.PI / 180) * val;
        }
    }

How to use this class?

            GeoCoordinate g1 = new GeoCoordinate();
            GeoCoordinate g2 = new GeoCoordinate();

            g1.Latitude =-29.83245;
            g1.Longitude = 31.04034;

            g2.Latitude = -51.39792;
            g2.Longitude = -0.12084;

      var geotool = new GeoCoordinateTool();
      var distance = geotool.Distance(g1, g2, 1);

Here are technical references for the formulas:

• The Haversine Formula (Assume Earth is spherical)
  
• The Vincenty's Formula (More Accurate;Using Theoretical Ellipsoid for Earth)

search texts: easiest way to calculate a distance, example of using GetDistanceTo, without Google Maps API