Example.

We can say 245/50/17 is wider than 225/50/17.

But 225/50/17 is the same as 235/60/17.

* My math and examples may be off, but I hope you see the question I'm asking. And I'm not using any of these sizes. It's just the example to set up the question.

Is there a formula to calculate the actual tire's contract patch?

 

Put a sheet of paper under the front and back of the tire as far as it will go. Measure the distance between the paper, then do the same for the inside and outside of the tire. Multiply those numbers to get the sq in. The contact patch is determined mostly by the weight of the car. Putting a much wider tire on a car doesnt actually increase the contact patch as much as you would think. Say you have a car with 205 width tires and you put on 255. The weight of the car pressing down is only going to force a certain amount of tire to touch the road, assuming correct inflation. With the wider tires you will have a wider, shorter patch vs a narrower tire that would have a narrower, but longer contact patch.

 

There's no formula, but the Tire Rack has tire specs that show the tread width, in addition to the section width (which is the first number in the tire size).