Rubin Boxer's "Engineering Analysis Of Thoroughbred Racing" explains in detail how to compute the extra distance traveled by horses running outside the rail position. To compute the extra distance a horse runs from the outside post:

Multiply the distance, in feet, to the turn from the starting gate by itself.
Multiply the distance, in feet, from the outside post to the rail by itself.
Add the two together and take the square root of the result.

Example:

4f. to the turn = 2640' x 2640 = 6969600
75' to the rail = 75' x 75 = 5625
6969600 + 5625 = 6975225
SqRt of 6975225 = 2641.07'

Position from the rail around a turn

1 = .94 lengths
2 = 1.88 lengths
3 = 2.83 lengths
4 = 3.77 lengths
5 = 4.71 lengths