one would tend to assume a 40” screen is twice the size of a 20” screen, but the screen size is proportional to the square of the diagonal length (i.e. Area = k*h²). this is easy to do mentally for multiples (e.g. 40” is twice as long as 20”, so the 40” screen is 4 times bigger) but I wanted to simplify the calculation for calculating any screen size.
below I have the proportionality constants (k) and the formula used to calculate it
- for 16:9 (widescreen tv's) use A = 0.427 * h²
[k=(16 / 9) * (sin(arctan(9 / 16))^2) = 0.427299703]
- for 16:10 (widescreen monitors) use A = 0.449 * h²
[k=(16 / 10) * (sin(arctan(10 / 16))^2) = 0.449438202]
- for 4:3 (old tv's and monitors) use A = 0.48 * h²
[k=(4 / 3) * (sin(arctan(3 / 4))^2) = 0.48]
one interesting thing is that, for the same reported screen size, older 4:3 tv’s will actually be 12% bigger. this is not very helpful, however, since most tv/movies are now presented in 16:9, and 4:3 tv’s will need to use the black bars and actually end up with 25% smaller pictures for the same reported screen size.
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