you asked for math, here it is

just remember there are few measurement definitionss to consider, with a simple lens.

Focal length (Fl) = the distance from the focusing plane for a subject at infinity

Subject distance(Ds) = the distance from the subject to the lens

Image distance(Di) = the distance from the lens to the focus plane (when focused at infinity Image distance = focal length)

lens extension (Le) = the distance the lens is extended forward (i.e. further away from the focusing plane) to focus at an object that is not at infinity. At infinity lens extension = 0

now for all lenses remember that when focused at any distance

1/Fl = 1/Ds +1/Di (you can see that at infinity the image distance is equal to the focal length)

You also need to consider that for a subject of height S the image height I is the ratio of Di/Ds = I/S, and I/S is the magnification ratio.

so now, if you want to add extension tubes to any lens,

1/Fl = 1/Ds +1/(Fl+Le)

or 1/Ds = 1/Fl +1/(Fl+Le)

this now gives you the working distance i.e. distance to subject(Ds) and if you consider the ratio of (Fl+Le)/Ds you get the magnification ratio of the lens (M).

You will get 1:1 Macro when Fl=Le and Ds=2Fl

Keep these formulas in mind and you can calculate your working distance and magnification ratio.

You can aslo consider adding diopters in front of a lens. the way a diopter lens works is the diopter number is 1/Fl, and by adding a diopter lens in front of any lens, the impact is that the infinity focus point is now the focal length of the diopter you add in front.

The lens focal length also changes, such that 1/Fl* = 1/Fl+diopter value where Fl* is the new focal length of the lens plus diopter, and the lens now has a permenant lens extension of Fl-Fl*

As a result, with the lens set at infinity the magnification ratio with a close up diopter lens is

M = Fl / (1/Diopter) where the Fl is the origonal lens focal length at infinity and 1/diopter is the working distance at infinity

Look at the formulas and you will see how simple it all is