# Calculating area volume from longitude, latitude and altitude

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hye wook Kim on 10 Sep 2021
Commented: Walter Roberson on 18 Sep 2021
Hello! I'm trying to calculate the volume of airspace(3d polygon) from its longitude, latitude and altitude.
The polygon's vertices are given with longitude and latitude (ex. [128 129 129 128 128], [37 37 38 38 37])
and its altitude ranging from 1000~5000 feet.
How can I get the volume of this 3d polygon?

darova on 11 Sep 2021
• Convert spherical coordinates into cartesian using sph2cart
• Use alphaShape to build an object and calculate volume
Walter Roberson on 18 Sep 2021
You need to change the 1000 and 5000 to "radius of the Earth in that area, in feet, plus this".
Latitude at 37, Earth radius at sea level: 3958.404 miles
Latitude at 38, Earth radius at sea level: 3958.18 miles
That is a decrease of
format long g
(3958.404 - 3958.18) * 5280
ans =
1182.72000000085
a bit over 1000 feet. So 1182.72 feet at 38 degrees (which is within the airspace) would be at sea level at 37 degrees (and so not in the airspace.)
So, you cannot treat the base of the airspace as flat: the curvature difference is equal to approximately 1/4 of the difference in altitudes between the 1000 and 5000 foot level.
That page gives a radius equation that it might be useful to integrate over.
R = √ [ (r1² * cos(B))² + (r2² * sin(B))² ] / [ (r1 * cos(B))² + (r2 * sin(B))² ]
Integrate altitude + R over altitude and latitude in radians, and multiply by radians spanned by longitude, to get volume.