Calculate Earth convex hull polygon area given latitude and longitude

Question

I have searched for explanations and algorhitms how to calculate Earth's polygon surface area. I've found this and this
Lets say I got already convex hull points
[56.992666,24.126051], [58.00282,25.930147], [58.787955,25.565078], [59.4997,24.861427], [59.463678,24.711365], [59.395767,24.599837], [56.992666,24.126051]

From second link the first answers uses Python library and second answer approach won't give quite precise area even if we assume that Earth is sphere (am I right)? What approaches could I take for calculating the area (less expensive) if we assume that Earth is sphere?

In addition, I have looked for different libraries (geotools.org etc) but haven't found in their documentation about area calculation.

This looks useful: http://forum.worldwindcentral.com/showthread.php?t=20724 — TreyA, Mar 07 '12 at 17:46
And this was referenced in the worldwind thread: http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/40409/1/07-03.pdf — TreyA, Mar 07 '12 at 17:51
@TreyA Thank you very much for directions! Reading the PDF now. Sadly the algorhitm in the forum post gave me totally wrong answer. I checked answer here http://www.daftlogic.com/projects-google-maps-area-calculator-tool.htm with my points and correct one is ~15200km2 but the algorhitm gave over 5 000 000. The latitude-longitude pairs are in my post — Skyzer, Mar 07 '12 at 21:17
@TreyA Hey the algorhitm in the forum is working one. I forgot to convert my latitude-longitude degrees to radians beforehand. You can write your reply as an answer and i would accept that. — Skyzer, Mar 07 '12 at 21:48
@Skyzer In above link how to calculate spherical radius?. Is it earth's spherical radius if so which value to use for that?. Thanks in advance. — Narendra, May 04 '13 at 06:51

score 6 · Accepted Answer · edited Sep 26 '18 at 01:51

6

The algorithm for finding the area of a polygon on a sphere can be found here:
Thread: A method to compute the area of a spherical polygon

You could also use this NASA JPL paper for some algorithms:

Some algorithms for polygons on a sphere.

edited Sep 26 '18 at 01:51

Laurel

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answered Mar 08 '12 at 02:58

TreyA

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In above link how to calculate spherical radius?. Is it earth's spherical radius if so which value to use for that?. Thanks in advance. – Narendra May 04 '13 at 06:07
A typical value for the earth's radius is 6371km. – TreyA May 04 '13 at 11:44
thanks for your reply I was stalked on this. It means in above link we have to "Spherical radius = r (earth's radius)" and area will be in square kms? – Narendra May 04 '13 at 12:02
@TreyA NASA link broken. Any alternative ? – gansub Sep 16 '18 at 09:56

Calculate Earth convex hull polygon area given latitude and longitude

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