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

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.
http://mathforum.org/library/drmath/view/51879.html

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

Where
* 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);

// Intermediate result a.
double a = Math.Pow(Math.Sin(dLatitude / 2.0), 2.0) +
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;

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).

Thanks...
0
rmmarsh
1 Solution

Commented:
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?
0

Author Commented:
Unbelievable... I see it... thank you so much!
0

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