What is the formula for migration rate of DNA in agarose gel electrophoresis?
I guess my answer is very old, but here it is for newcomers searching the internet for this formula:

$$D = a - b \log(m)$$ 

where


$D$: Distance traveled for the restricted fragment.
$a$ and $b$: Constants depend on the electrophoresis experiment. 
$\log(m)$: The logarithm of the molecular weight ($m$)of the fragment.


Knowing $a,b$ and the distance traveled in your gel, you can easily determine the molecular weight of your fragment and its size by the following formula:

$$m = e^ \left(\frac{a-D}{b}\right)$$