What's the unit of area being calculated in S2Cell class?

[chhabraamit]

Level 0's average area is 2.0943951023931953 and 4 times of it is supposed to cover the entire Earth's area.

[placz]

It's measuring the surface area on a unit sphere covered by the cell. 6 times a level 0's average area is 4 * pi. (6 sides on a cube, not 4)

[datamacgyver]

To add context here (because I got here and scratched my head for a bit):

• S2 assumes the earth is a perfect sphere
• The surface area of a sphere is given by 4*pi*radius.
• If we assume radius is 1 ("a unit") then the surface area of a sphere is simply 4*pi, or 12.5664...
• Note that 12.5664 / 6 (the six sides of the cube!) = 2.0944... which is the number you have
• As we've not got a unit for our radius of one, our number also has no unit so in answer to your explicit question: There isn't one!

Now, your implicit question of how we obtain something that we can interpret more easily:

• I know that the total area of one cube face given by S2's authors is 85,011,012.19 km^2
• If 2.0944... = 85,011,012.19 then 1 = 40,589,768.4219... km
• Therefore, to convert to km^2 I multiply an S2 area by 40,589,768.4219...
• I have not validated the accuracy of this compared to a projection of a polygon but it's in the ballpark based on me drawing squares over the middle east. It'll never be perfect as the Earth is pretty far from a perfect sphere!

Please correct me if I'm wrong, this makes sense in my head. Oh, and I've been liberal on the rounding here! Your mileage will vary but I'd advise working the above out to a precision that fits your use case!

[eengle]

The unit of measure, when the sphere is radius 1, is called a "steradian", basically the spherical equivalent of the 2D radian. It has the nice property that a number 10% the size of the whole 4*pi value is in fact 10% of the land area, so it's linear with the size of the surface being covered.

[eengle]

I'm closing this but feel free to reopen if there are any other questions about this.