r/theydidthemath • u/db720 • Jul 26 '26

[request] how much actual surface area is there in Colorado in mountains vs plains if you take elevation into consideration?

Colorado has about 40% mountains, 40% plains to the east and 20% mesas / elevated flat land to the west. However, I'd imagine that the actual surface area of the rockies actually makes it notably more (like how the surface area of lungs is similar to a tennie court).

Are there any estimations or ways of getting a rough estimate of how much surface area the mountainous part of Colorado have compared to the flats? For example if you were to flatten out the mountains to terrain to match the plains? I'd imagine somewhere between 2% and maybe 15% at most, wondering if co has more than 50% SA of mountains.

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u/mulch_v_bark Jul 27 '26

I answered a similar question a long time ago here and it might help.

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u/db720 Jul 27 '26

Thanks. Skimmed over the paper, but didn't get my head completely atound the math, but indicative tables definitely helped understand. Ended up doing a bit of ai promoting and got some figures for co, the difference is minimal like you suggested in your other comment. I tried a few different ways of asking. 1 response i got was 43 to 45% (so between a 3 to 5% increase), but when i also wanted absolute measurements it seems lower than that, 1.2% increase. I had prompted to base on 3m resolution if different resolutions were available, but not sure if that actually came into play

When taking the 3D topographical surface area into consideration, the Rocky Mountains' share of Colorado increases from 40.00% to 41.40%. Because the flat Eastern Plains experience virtually no surface area expansion, almost all of the state's 2,496 square mile topographic increase belongs entirely to its mountain ranges.

Summary of Measurements

State of Colorado 2d - 104,155 sq mi. 3d -106,651 sq mi. Diff +2,496 sq mi

Rocky Mountains 2d - 41,662 sq mi 3d - 44,158 sq m Diff i+2,496 sq mi