I started with a formula from Ace Hardware.
This formula only takes into account the square footage of the room. I decided that the height of the room ought to be factored in, so I added a dimension and then divided the multiplier by 10 (assuming that they assumed an average room to have a ten-foot high ceiling).
Again, this is just a rough estimate. Ace Hardware may have rigged the formula to sell more-powerful-than-necessary (and therefore more expensive) air conditioners, but I did compare this formula with formulae on other websites and found it to be about right.
The Association of Home Appliance Manufacturers offers a more complete formula that includes sun exposure, insulation levels, and a variety of other variables. There is another, simpler calculator from This Old House.
If I use the later to calculate the necessary cooling capacity for the same hypothetical 12' × 20' × 10' room, with a southern exposure, no kitchen, insulation, and direct sunlight, it results in the same 10,000 BTU estimate.