There is and it's complex:-
Suppose you have a lens of focal length F which can focus down to distance X when mounted on your camera. Suppose you use an extension tube of length L. Then you can focus down to the distance given by the formula
F(XF +XL - Lf)/(XL -LF +f^2)
In words, you do the following. First multiply the shortest distance by the focal length, the multiply it by the tube lenth and then multiply the tube length by the focal length. Add the first two numbers and subtract the third. Then multiply the result by the focal length. That gives you the numerator.
Next take the product of the shortest distance by the tube length and the product of the tube length with the focal length, both of which you already calculated, subtract the second from the first, and then add the square of the focal length. That gives you the denominator. Divide the numerator by the denominator, and you are done.
I looked at that back in my 35mm days. You'll spend more time doing maths than taking pics. I think trial and error is a bit easier.