I am thinking about getting some shorter tires to run on the rear of my dart at the track. Is there a formula to figure how much an inch changes your rear "gear ratio"?

It's strictly a ratio thing. If the original tire is 26" and the new tire is 25" 26/25=1.04. Multiply that by your existing rear axle ratio to get the new effective ratio. Say I swap my 26.1" tall 205/75R14s with 25" tall 255/40R17s and I have 3.21 gears. 26.1/25x3.21=3.35

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Joshua

Allen and I do this all the time and it works well with cars you have to drive to and from the track.

We did it on the 66 Dart wagon for this year's Vegas race, have the 3.07 gears in the rear with a tall 27 inch tire, that combo tows well at 65-75 mph.
Swapped on some well worn 50 series that are a pinch under 24 inches tall and the effective ratio went to 3.45
The car pulled better and never spun at the starting line. (20 psi)
You see a lot of cars at the track that use this "trick".
DD