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How do I compute the distance between two locations using GPS coordinates?

Posted on 2006-06-20
Medium Priority
Last Modified: 2012-06-27
I have a program that needs to compute the distance between two locations using their GPS coordinates.  I had attempted to use the Halverson formula, but my calculations are off by many miles, almost 30%.  My code (in C#) is as follows:

        private double Calc(double Lat1, double Long1, double Lat2, double Long2)
                The Haversine formula according to Dr. Math.
                dlon = lon2 - lon1
                dlat = lat2 - lat1
                a = (sin(dlat/2))^2 + cos(lat1) * cos(lat2) * (sin(dlon/2))^2
                c = 2 * atan2(sqrt(a), sqrt(1-a))
                d = R * c
                    * dlon is the change in longitude
                    * dlat is the change in latitude
                    * c is the great circle distance in Radians.
                    * R is the radius of a spherical Earth.
                    * The locations of the two points in spherical coordinates (longitude and latitude) are lon1,lat1 and lon2, lat2.

            double dDistance = Double.MinValue;
            double dLat1InRad = Lat1 * (Math.PI / 180.0);
            double dLong1InRad = Long1 * (Math.PI / 180.0);
            double dLat2InRad = Lat2 * (Math.PI / 180.0);
            double dLong2InRad = Long2 * (Math.PI / 180.0);

            double dLongitude = dLong2InRad - dLong1InRad;
            double dLatitude = dLat2InRad - dLat1InRad;

            // Intermediate result a.
            double a = Math.Pow(Math.Sin(dLatitude / 2.0), 2.0) +
                       Math.Cos(dLat1InRad) * Math.Cos(dLat2InRad) *
                       Math.Pow(Math.Sin(dLongitude / 2.0), 2.0);

            // Intermediate result c (great circle distance in Radians).
            double c = 2.0 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1.0 - a));

            // Distance.
            // const Double kEarthRadiusMiles = 3956.0;
            const Double kEarthRadiusKms = 6376.5;
            dDistance = kEarthRadiusKms * c;

            return dDistance;

        //-----------------    computes distance using direction    ---------------------
        public double Calc(string NS1, double Lat1, double Lat1Min, string EW1, double Long1, double Long1Min,
            string NS2, double Lat2, double Lat2Min, string EW2, double Long2, double Long2Min)
            //  usage: ComputeDistance.Calc(" N 43 35.500 W 80 27.800 N 43 35.925 W 80 28.318");

            double NS1Sign = NS1.ToUpper() == "N" ? 1.0 : -1.0;
            double EW1Sign = NS1.ToUpper() == "E" ? 1.0 : -1.0;
            double NS2Sign = NS2.ToUpper() == "N" ? 1.0 : -1.0;
            double EW2Sign = EW2.ToUpper() == "E" ? 1.0 : -1.0;

            return (Calc( (Lat1 + (Lat1Min / 60)) * NS1Sign,
                (Long1 + (Long1Min / 60)) * EW1Sign,
                (Lat2 + (Lat2Min / 60)) * NS2Sign,
                (Long2 + (Long2Min / 60)) * EW2Sign

Can someone please tell me where my error is?  (I am not a math major, nor anywhere close to one).

Question by:rmmarsh
LVL 85

Accepted Solution

ozo earned 2000 total points
ID: 16945052
maybe this is too obvious but you say you are off by many miles, while your calculation is in kilometers
Or can you give an example of a wrong calculation?

Author Comment

ID: 16948294
Unbelievable... I see it... thank you so much!

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