*"...using formulas" - feliperodrigosek*

Closed form equations are notoriously difficult to come by in the inductance and capacitance realms. Sometimes there are trivial solutions for toy situations that have a lot of symmetry, but for real situations you end up relying on FEA (finite element analysis) or on real-world data obtained via experiment.

First order, capacitance is proportional to the plate area and the inverse distance between them. Inductance is proportional to wire length. Beyond that things get hairy. Capacitance as seen by the Theremin is a combination of variable intrinsic (antenna and the universe) and variable mutual (antenna and the hand). If you do FEA you'll see that the intrinsic decreases and the mutual increases as the hand approaches (as more and more lines of force from the antenna switch from landing at infinity to landing on the hand) with the net result a rather advantageously musical functional response (roughly exponential heterodyned frequency).

If you are using a simple LC oscillator you can work backwards from the resonance equation F = 1 / [2 * pi * sqrt(L * C)], where the C is the parallel combination of any physical component C and the antenna intrinsic + mutual. The antenna intrinsic + mutual is the hard part, though to a first order you can use the inverse distance times a constant plus an offset.

If you take everything into account via various rules of thumb and such you may end up with a 90% correct answer, or even 99%, but probably not 100%. It's definitely a diminishing returns type thing, where the more work you put into it the less you get back.