Depends on what is the maximum stress you're going to allow your beam to carry.
Since I don't know what material you're dealing with, I can't recommend stress values.
stress = Mc/I, where M is maximum moment across the beam, c is distance from bending centroid to the most outer face of beam, and I is the moment of inertia.
Plug in the desired max stress and solve for your c or I, and make/construct your beam to match.
Another method to find beam size is to do it by knowing the maximum deflection in the beam you're willing to have. But this is another animal entirely, and there's no "simple formula" you're looking for.
Above method will work with timber and, in a simplified way, steel. Hopefully you're not using concrete. Concrete is a non-linear material and you'll need an engineer to do it.
Have fun!
A CivEng from US.