Assuming a linear potentiomenter and straightforward mechanical motion, the formula is just the equation for a line:
y = mx + b
Read the voltage as
x.
Multiply it by a scaling constant
m.
Add an offset constant
b.
The corresponding angle is
y.
To determine the constants, read the voltage at two known angles. Put the voltage and angle in for
x and
y. Now you have two equations with two unknowns, and you can solve for
m and
b.
Or you can do what Garrett suggests and not worry about angles at all. Just use voltage in your programming. You don't need to say "put the angle at 30 degrees". You can say "move until the voltage is 1.36" instead.