This issue keeps coming up and won't go away. There are lots of Tire Calculators posted on line, and they all produce the wrong answer for "Turns Per Mile".

The common method is to multiply the specified tire section width by the aspect ratio to get sidewall height, which is correct by manufacturer specification. For example, 165-80-15 tire says 165-mm width x 0.80 aspect ratio gives 132-mm (5.20-inch) sidewall height for a free standing unladen tire.

A 15-inch wheel rim plus two sidewall height gives 15+5.20+5.20=25.4-inch overall tire diameter,which is also correct.

Multiply tire diameter by Pi to get tire circumference: 25.4x3.1416=79.80-inches, also correct.

Then take inches in a mile and divide by tire circumference to get Turns Per Mile: 63360/79.80=794. This is mathematically correct, but is the wrong answer in the real world.

The correct number is more like 806 Turns Per Mile, about 1.5% higher than calculated. Reason for this error is because a tire with air pressure inside and a load on it against the ground does not roll like a simple mathematical circle.

When a tire is loaded it gets smashed flat on the bottom with a contact patch about the size of your hand, also bulging out on the sides,no longed a round circle. The rotational axis (center of the axle) is closer to the ground, reducing he rolling radius, but still not the whole story.

There is an intuitive way to think of this. Most modern tires have a tread belt embedded in the carcass, as in "steel belted radial tire". The belt can be various materials, but in general the belt will be quite rigid and does not deform, except to lie flat and parallel to the road surface. As a result, the travel distance for one turn of the tire will be closer to length of the belt.

Diameter of the belt is of course less than overall diameter of the tire.You can calculate the belt diameter (sort of) or the rolling diameter as a ratio of calculated TPM divided by actual TPM, times the free OD of the tire. In this case, rolling diameter= 794/806 x 25.4 = 25.0". Think of the belt lie about 0.20" below the outside surface of the tread, which is the foundation of the 1.5% error in calculated "Revs Per Mile".

This depends on tire type. Snow tires or off road tires with greater tread depth will have the belt positioned deeper below the OD (smaller belt diameter). Oddly enough, tread wear reduces tire OD, but has very little effect on travel distance, because the belt does not change length. So a tire giving 806 TPM when new will still give 806 TPM when worn out to end of life, so the speedometer and odometer readings do not change much with tread wear. Surprise!

Part of the trick to calculating actual TPM lies in knowing where the belt lies in the carcass. Tire manufacturers will never publish this parameter, but they do often publish the TPM number, because it is otherwise near impossible to calculate. But for sure, the rolling diameter of a tire is always less than the free outside diameter, which is why all of the existing tire calculators give incorrect answer for Turns Per Mile.

However, Tread depth is very often published, or it can be measured directly on a new tire. You can do something kind of capricious, like subtract 2/3 of the tread depth from the free outside radius of the tire to get closer to the loaded rolling radius. Or subtract 4/3 of the tread depth from OD of the new tire to get loaded rolling diameter. This is a simpler calculation that can give a better result, and easy enough to add "Tread Depth" to input data for the tire calculator. Still an approximation, but it should work as well for off road tires or racing slicks (with tread depth holes in the slick tread surface). This could be better than just re-publishing the same OD calculator that always under-estimates Turns Per Mile.

Food for thought.