[Django]-Calculating distance between two points using latitude longitude and altitude (elevation)

You can calculate distance between flat coordinates in, say, meters by using geopy package or Vincenty’s formula, pasting coordinates directly. Suppose the result is d meters. Then the total distance travelled is sqrt(d**2 + h**2) where h is the change in elevation in meters.

EDIT 2019: Since this answer, I composed a Q&A style example to answer similar questions (including this one as an example): How to calculate 3D distance (including altitude) between two points in GeoDjango.

In sort:

We need to calculate the 2D great-circle distance between 2 points using either the Haversine formula or the Vicenty formula and then we can combine it with the difference (delta) in altitude between the 2 points to calculate the Euclidean distance between them as follows:

dist = sqrt(great_circle((lat_1, lon_1), (lat_2, lon_2)).m**2, (alt_1 - alt_2)**2)

The solution assumes that the altitude is in meters and thus converts the great_circle‘s result into meters as well.

You can get the correct calculation by translating your coordinates from Polar (long, lat, alt) to Cartesian (x, y, z):

• Let:
  polar_point_1 = (long_1, lat_1, alt_1)
  and
  polar_point_2 = (long_2, lat_2, alt_2)

• Translate each point to it’s Cartesian equivalent by utilizing this formula:

  x = alt * cos(lat) * sin(long)
  y = alt * sin(lat)
  z = alt * cos(lat) * cos(long)
  

  and you will have p_1 = (x_1, y_1, z_1) and p_2 = (x_2, y_2, z_2) points respectively.

• Finally use the Euclidean formula:

  dist = sqrt((x_2-x_1)**2 + (y_2-y_1)**2 + (z_2-z_1)**2)
  

I used the solution provided by John Moutafis but I didn’t get a right answer.The formula needs some corrections. You will get the conversion of coordinates from Polar to Cartesian (x, y, z) at http://electron9.phys.utk.edu/vectors/3dcoordinates.htm.
Use the above formula to convert spherical coordinates(Polar) to Cartesian and calculate Euclidean distance.

I used the following c# in a console app.
Considering following dummy lat long

       double lat_1 = 18.457793 * (Math.PI / 180);
       double lon_1 = 73.3951930277778 *(Math.PI/180);
       double alt_1 = 270.146;

       double lat_2 = 18.4581253333333 * (Math.PI / 180);
       double lon_2 = 73.3963755277778 * (Math.PI / 180);
       double alt_2 = 317.473;

       const Double r = 6376.5 *1000; // Radius of Earth in metres

       double x_1 = r * Math.Sin(lon_1) * Math.Cos(lat_1);
       double y_1 = r * Math.Sin(lon_1) * Math.Sin(lat_1);
       double z_1 = r * Math.Cos(lon_1);

       double x_2 = r * Math.Sin(lon_2) * Math.Cos(lat_2);
       double y_2 = r * Math.Sin(lon_2) * Math.Sin(lat_2);
       double z_2 = r * Math.Cos(lon_2);

       double dist = Math.Sqrt((x_2 - x_1) * (x_2 - x_1) + (y_2 - y_1) *    
                               (y_2 - y_1) + (z_2 - z_1) * (z_2 - z_1));