Okay, lets start out with some basic info. LCD sizes are given as a diagonal measure, that is, top left corner to bottom right corner. These sizes should always be taken as approximate, since they're seldom exactly the size specified, particularly in inches.

Common LCD aspect ratios are 4:3, 5:4, 15:9, 16:9, and 16:10

4:3 is common for 15" 1024X768 LCDs, PSOne, XBox and such for small format 320X240 LCDs. Also can be used for QXGA (2048X1536) LCDs

5:4 is pretty much used for 17" and 19" LCD monitors, 1280X1024 resolution.

15:9 is used for some widescreen LCDs, typically the 1280X768 resolution.

16:9 is used for wide-screen TVs, and portable DVD players with the 480X234 resolution.

16:10 is used for other widescreen LCDs, like the 1920X1200 WUXGA screens.

First step is to determine which you have.

Use pythagorean theorum to determine a factor for the diagonal area. Use c^2 = a^2 + b^2 where a and b are the numbers from your aspect ratio. Using the 4:3 as an example:

c^2 = 4^2 + 3^3
c^2 = 25
c = 5

Now we take a and b and divide them by this number, which gives us a factor for how large each size is, relative to the diagonal measurement.

4 / 5 = 0.800
3 / 5 = 0.600

So for a 15" LCD, the horizontal is 15" * 0.800 = 12" and the vertical is 15" * 0.600 = 9"

So the factors for:

4:3 - a=0.800 b=0.600
5:4 - a=0.781 b=0.625
15:9 - 1=0.824 b=0.495
16:9 - a=0.872 b=0.490
16:10 - a=0.848 b=0.530

These factors can be applied to your LCD screen, or, once you have a projected screen size from the focal calculator, you can apply the same factors to that number, to have an idea of how large your projected screen will be.