Why a size change breaks your speedometer

Why it happens

Your speedometer doesn't measure road speed directly. It counts rotations — of the wheel, or a sensor further up the drivetrain — and multiplies by the rolling circumference the vehicle was calibrated with at the factory. That calibration is baked in and assumes one specific circumference: the stock tire's.

Swap in a tire with a different overall diameter and every rotation now covers a different distance than the speedometer assumes it does. The wheel doesn't know anything changed. The speedometer keeps doing the same multiplication with the old number, so the answer it displays is wrong by exactly the same ratio the diameter changed.

The math

Actual speed = indicated speed × (new diameter ÷ old diameter). Rolling circumference is π × diameter, and both the old and new circumference share that same π, so it cancels out of the ratio — you never need to compute circumference at all, just the diameter ratio.

A tire's overall diameter comes from two numbers on the sidewall: rim diameter (in inches) plus twice the sidewall height. Sidewall height is section width × aspect ratio ÷ 100, converted from mm to inches. That's the whole formula — no trigonometry beyond a circle's circumference.

Worked example

265/70R17 has an overall diameter of 31.61in. Go to 285/70R17 and it's 32.71in — a 3.5% increase. Multiply: 60 × 1.0349 = 62.09, which is the 62.1 the calculator reports.

Go the other way — say you're running 285/75R16 now and you're moving back down to a more street-friendly 265/75R16 — and the same math runs in reverse. Diameter drops 3.6%, and now the dash reads higher than you're actually going:

Same formula both times. Bigger tire, dash reads low. Smaller tire, dash reads high. The direction isn't a rule you memorize — it falls straight out of the diameter ratio.

Does it actually matter?

Yes, in three concrete ways:

Speeding. With a larger tire, actual speed reads higher than indicated. If your dash says 60 in a 60mph zone, you're already doing 62.1 in the 265/70R17 example above — a margin you didn't ask for and don't know is gone.

Cruise control. It targets the same wrong rotation math the speedometer displays. Set it to an indicated 70 with that tire on and you're actually holding 72.4, the whole trip.

The odometer. It accumulates the same ratio error over distance instead of speed. Drive a real 12,000 miles on the 265→285 setup and the odometer only shows about 11,596 — 404 miles it never counted. Mileage-based service intervals and warranty limits get reached later than the odometer suggests, and resale mileage reads a little low relative to actual wear. Run the smaller-tire example and it flips: the odometer overcounts, by roughly 448 miles over the same 12,000.

What changes together with your speedo

Speedometer error is a direct function of diameter change and nothing else — offset, backspacing, and wheel width don't touch it. If keeping your speedo accurate is the goal, see plus-sizing for how to pick a size that holds diameter close to stock. If you're chasing a fitment change instead — more poke, less poke, different backspacing — that's a separate question with its own math, covered in offset and backspacing.