It depends a lot on how big these things are. If very tiny then testing and measuring is the only way to get something approaching accurate results.
If you are talking say, 1/2" diameter and up then things change a little, but it still, ultimately, is going to come down to testing.
Your assumptions with the full circle are a little off in that the force is applied in a single plane, albeit from opposite directions. That means said force will be applied in that direction. There will be greater force acting at the horizontal center-line than at points around the circumference. The applied force will diminish (effectively) to zero at the vertical center-line.
What are you trying to achieve? Holding by force is not the first choice for holding anything.