How Extension Tubes Affect Magnification
Prepared 2007-02-02 (169/12612) by Bill Claff

The following formula governs the mathematics of achieving closer focusing and increased magnification by using extension tubes or close-up lenses.

v = ( 1 + m ) * f

Where:
v is the distance from the rear principal plane of the lens to the focal plane
m is magnification
f is focal length

Note that it is common for the focal length of a lens to decrease as you focus closer than infinity.
See Estimating Focal Length at Closest Focus for details on estimating the closest focus focal length.

Using the result of the above referenced post for the 300mm f/4D ED-IF AF-S Nikkor we have the following values:

 focus f v m infinity 300mm 300mm 0 closest 242.9mm 308.5mm .27

Note that in addition to reducing focal length there is a slight internal extension of this lens during focusing.

We can rearrange the formula for v to solve for m

m = v / f - 1

It's clear from this formula that if we increase v by x them m increases by x / f, ie.
mx = ( v + x ) / f - 1 = m + x / f

So, if we add 68mm of tubes to the above example

 focus x / f mx S infinity .23 (68/300) .23 (0 + .23) 1973mm closest .28 (68/242.9) .55 (.27 + .28) 1061mm

The values for S come from sticking mx and f back into the formula

S = ( 1 / m + 1 + 1 + m ) * f

So, in other words, with 68mm of extension this lens will focus on subjects between 1061mm and 1973mm away.
At 1061mm the magnification will be .55x and at 1973mm the magnification will be .23x