The distance calculation is the diagonal size of the screen times the throw ratio of the projector (x/12 for feet).
If the projector has a physical zoom this plays in as well, throw ratios are usually displayed at 1x or for the whole range (e.g. 82C; 1.2 zoom means 1.43-1.71 throw).
Light calculations are somewhat inside the scope of this question, but suffice it to say, they aren't fun to do IMHO which is why I like the online calcs for a quick reference. Rule of thumb, the brighter the room or bigger the picture, the brighter the need.
If you don't want to do the calculations yourself, there are hundreds of calculators out there. Projector Central has a good distance calculator that is preset for actual projector specs. I use it often so I don't have to mess with the calculations. Just go to their website and select "Calculator Pro" at the top. It even does estimated light readings (we aim for 80fL because of the bright room environment we have to deal with, but for controlled lighting 30-50 is a good range too.)
There are also apps available on Android and iOS like AV Tools or Alford Calc.
If you want to do precise calculations, you need to know the size of your screen, the throw ratio of the projector and the brightness of the projector (and the brightness of the room) and the reflectivity of the surface (gain).
The latter two of these deal with picture intensity, the fact as your image gets smaller, the image gets brighter; to a point that it can be uncomfortable to watch. The opposite is also true, that as the the image gets larger, it gets darker since the amount of light coming from the projector doesn't change.
And finally, the more ambient light in the room, the darker or more faded the image will appear as it competes with other light sources.
on May 22, 2014