A more concrete example: You discover that the formula for making a beam that will have equal stress all along it's length is t = (.923)Xe/L^2 (made-up formula)

You can not patent that formula, but you can get a patent on beams made using that formula. With that patent in hand you can stop anyone from making, selling, or using those beams.

Sounds like a distinction without a difference. If you can stop people from using a formula with your patent, you've effectively patented that formula.