I think I've figured out what you're

*trying* to say. But what you did say implies that you think by measuring how far down a bearing goes, you can measure the diameter of the hole.

measuring how deep it falls into the hole....

I can take a 1" drill bit and drill a hole 6" deep or 12" deep. The bearing is going to fall a lot further in the 12" deep hole, and have nothing to do with the diameter.

What I *think* you mean is that the bearing sits on the hole and doesn't fit down into it. There may be an easy/easier formula, but it's not something I've ever used. What you can do is use the formula for a sphere, then find a formula for the trace (cross section) of the sphere at any point. x^2+y^2+z^2=r^2. If your radius is 0.1, and the top of the sphere is .163 units above the surface, then you're looking for the formula for the circle at a value when z=-0.63 (The surface is 0.63 units below the center of the sphere.) So, plug -0.63 into the equation for z, plug in 0.1 for r, and do a little arithmetic so that it says x^2+y^2 = some number. The square root of that number is the radius of the hole.

Alternatively, if your bearing is very hard, you could smack it really hard with a hammer a few times. Then, the radius of your hole is 0.1.