Overall diameter, loaded radius and rolling radius differ

Run 275/70R18 through the arithmetic and it returns 33.16 in of overall diameter, a circumference of 104.2 in and 608.3 revolutions per mile. Those figures are exact, and they describe a tire that is inflated, unloaded and stationary.

Put the tire under a vehicle and none of the three survives unchanged. Which is fine — as long as you know which of the several radii a given question is actually asking about.

Free radius

Half the overall diameter, measured on the specified rim at the specified pressure with no load on it. This is what a size code yields, what tire manufacturers publish as "overall diameter", and what every calculation on this site computes.

It is the right number for comparing two sizes, because it is the only one defined identically for both. It is also the number that governs the top of the tire — the part that meets a fender lip on compression, and the part nothing squashes.

Static loaded radius

Measure from the wheel centre to the ground with the vehicle's weight on the tire and you get a smaller figure. The casing deflects; the contact patch is flat rather than a point on a circle.

Manufacturers publish this alongside the free radius in their data books, and it moves with three things: load, inflation pressure, and how stiff the casing is. A light-truck casing at 65 psi deflects less than a passenger casing at 35 psi carrying the same load, which is why two tires with identical size codes can sit at noticeably different heights on two different vehicles.

This is the number that quietly breaks lift arithmetic. Half of a diameter increase is the geometric answer for how much higher the axle sits. It is right only if the new tire deflects by the same amount as the old one, and a taller tire is usually a stiffer, higher-pressure-rated one. The measured change at the axle tends to come out slightly larger than the calculator says.

There is a second reason the figure disappoints, and it is pure geometry rather than deflection. The other half of the diameter increase goes upward. A larger tire raises the body and closes the gap above its own crown by the same amount at the same moment, so every clearance measured from the tire to the arch gets worse by exactly what the axle gained. Raising a vehicle and fitting a bigger tire are two operations that move different things, and only one of them creates room overhead.

Pressure is the lever with the most authority here. Add air and the casing deflects less under the same load, so the loaded radius rises; let air out for traction on sand or rock and it falls sharply, which is the entire mechanism behind airing down. The free radius barely moves through any of it.

Dynamic rolling radius

Neither of the above governs distance travelled. Roll the tire one full revolution, measure how far it went, divide by 2π, and you have the dynamic rolling radius — the effective radius that produces the right answer for speed, odometer and revolutions per mile.

It sits between the free and loaded radii. The tread band is a steel-belted hoop that resists shortening, so the tire does not simply travel the circumference of its squashed profile.

This is why manufacturers' published revolutions-per-mile figures are measured, not computed, and why they usually come out a few percent above the geometric number for the same size. This site computes from geometry and says so, because a geometric figure derived identically for two sizes compares them honestly, whereas a mix of one measured and one computed figure does not. Revolutions per mile covers the conversion itself.

Growth at speed

Centrifugal force pulls the tread band outward, so a tire is slightly larger at 80 mph than at rest. The effect is small on a passenger radial and larger on a tall, soft-sidewall tire, and it is one reason a speedometer error measured at 30 mph does not extrapolate perfectly to 80.

Shrinkage over the tire's life

The most-ignored figure of all. Tread depth is part of the radius, and it is consumed.

A new all-terrain tire may start with 16/32 in of tread and be replaced at 4/32 in. That is 12/32 in — 0.375 in — gone from each side, so 0.75 in off the overall diameter. A worn tire at the end of its service life turns measurably faster than the same tire when new, drives the speedometer slightly higher, and covers slightly less ground per revolution.

Practical consequences:

• A pair of new tires and a pair of half-worn ones of the same size do not have the same circumference, which matters on all-wheel-drive vehicles and limited-slip axles.
• A speedometer correction calculated on new tires drifts back the other way as they wear.
• Clearance measured on a worn set gets tighter the day you replace them.

Which radius to use for which question

Question	Radius that answers it
Will this tire's crown reach the fender lip?	Free radius, plus growth at speed
How much higher does the axle sit?	Loaded radius, on both tires
What will my speedometer read?	Dynamic rolling radius, as a ratio between old and new
How many revolutions per mile?	Dynamic rolling radius
Which of two sizes is bigger?	Free radius — the only one defined the same way for both

What the arithmetic on this site is, precisely

Every diameter, circumference and revolutions-per-mile figure here is computed from the size code as free, unloaded geometry. That is a deliberate choice: it is reproducible, it is identical in method for every size, and it never mixes a measured value for one tire with a calculated one for another.

It also means these figures are not a prediction of what a tape measure will show against a loaded vehicle. For comparing sizes — which is what the comparison tool exists for — the geometric figure is the more honest of the two. For deciding whether something clears, the vehicle in your driveway is the only reliable measuring instrument, and a tire's own published specification sheet is the closest thing to a second opinion.