The great circle distance in degrees between Point1 (lat1, lon1) and Point2 (lat2, lon2) is easily calculated:

or what is the same:

In this paper we assume the following signs N=+, S=-, W=+, E=- .

cos(D) will always fall in the range -1 < cos(D) < 1 and (D) will be a positive angle: 0� < D < 180�. You can use a formula that will use the arctan function but this will give a result in the -90� to +90� range and you need to add 180� if the result is negative.

• multiply D by 60 to obtain distance in nautical miles or
  
• multiply D by 69 to obtain distance in statute miles or
  
• multiply D by 111.12 to obtain distance in Km

Azimuth

The azimuth or initial course from point 1 (origin) to point 2 (destination) Zn can also be easily calculated. Zn is always measured from North to East from 0� to 360�. First we calculate Z. If we have considered West longitudes as positive we use this formula:

                           Sin(lon2-lon1)                      
   Tan(Z) =  --------------------------------------------------
             sin(lat1) * cos(lon2-lon1) - cos(lat1) * tan(lat2)

(If we had considered East longitudes as being positive we would need to change the sign on one side of this equation.)

The function ATAN( ) returns a value between -90� and +90� so Z needs to be adjusted to the right quadrant in order to obtain Zn: 0� < Zn < 360�

    If sign(sin(Z)) = sign(sin(lon2-lon1))
    Then Zn = Z + 180
    Else, If Z < 0
          Then Zn = Z + 360
          Else Zn = Z

Expressed in another way:

Zn	0� < lon2 - lon1	lon2 - lon1 < 0�
Z > 0	Z + 180	Z
Z < 0	Z + 360	Z + 180

The following formula adds 180� if needed to reduce Zn to the correct quadrant: