Speedometer calibration, and what a tire change does to it

A speedometer does not measure road speed. It counts wheel rotations and multiplies by a number somebody stored in a module, and that number was chosen for one specific rolling circumference.

Put a different circumference under the car and the stored number is now wrong by exactly the proportion those two circumferences differ by. Nothing else enters the arithmetic, and no sensor anywhere on the vehicle is in a position to notice.

The correction is one multiplication

actual speed = indicated speed × (new diameter ÷ original diameter)

Because circumference is π times diameter, the π cancels and diameters are sufficient. Going from 255/70R17 at 31.06 in to 285/70R17 at 32.71 in is a 5.32% increase, so an indicated 70 mph is really 73.7 mph. Step instead to 33x10.50R17 — barely wider, slightly taller — and 70 indicated becomes 74.4 mph, a 6.26% error.

The sign is the part people get backwards. A taller tire makes the vehicle travel further per rotation, so it is going faster than the instrument says: the speedometer under-reads. A shorter tire produces the opposite.

The factory margin you are spending

Speedometers are deliberately biased to read high. Under UN Regulation 39, which governs type approval across Europe and much of the world, the indicated speed must never be lower than the true speed, and may exceed it by no more than 10% plus 4 km/h. Manufacturers build in margin so that production tolerance, tire wear and a change of brand can never push a car into under-reading.

The practical effect on a tire change is that the first couple of percent of increase is absorbed by that bias rather than producing an error you would notice. A stock speedometer reading 2% high, fitted with tires 2% taller, reads roughly true. Beyond that the margin is gone and the error becomes real.

Measuring the error on your own vehicle

Two methods, both arithmetic rather than equipment:

• Against a satellite reference. Hold a steady indicated speed on a level road and compare with a GPS-derived figure. Do it at two speeds — 40 and 70, say — because a pure circumference error is a constant percentage, and anything that is not proportional points at something else.
• Against a measured distance. Reset the trip meter at a known distance marker and read it at the next. The ratio of recorded to actual distance is the same ratio as the speed error, since both come from the same pulse count.

Whatever percentage falls out applies everywhere. At 5.32%, an indicated 100 miles is really 105.3 miles covered.

The odometer moves with it, and that has consequences

The odometer is the same pulse count integrated over time, so it inherits the error exactly:

• Service intervals arrive later in real distance than the display suggests.
• A lease or warranty mileage limit is reached before the instrument says so — or after it, if the tires are shorter than stock.
• Fuel economy computed from indicated distance is wrong by the same percentage, in the direction that flatters a taller tire.
• Resale mileage on a vehicle that spent years on oversized tires understates the distance actually travelled.

What can be recalibrated, and how

• Modern vehicles with an electronic tire-size parameter. Many manufacturers expose a tire size or revolutions-per-mile value to the dealer's scan tool. Where that exists, correction is a configuration change, and the odometer, cruise control and transmission shift scheduling all follow it.
• Aftermarket programmers. Handheld tuners for common trucks write the same parameter, usually offering tire diameter and axle ratio fields together.
• Inline correction modules. A device between the speed sensor and the cluster that scales the pulse rate. Effective for the cluster; whether other modules see the corrected signal depends entirely on where it is spliced.
• Cable-driven instruments. On older vehicles the transmission turns a small driven gear whose tooth count sets the ratio. Changing that gear is the original recalibration, and it is genuinely mechanical — a different tooth count for a different tire size.

What none of them do is change the vehicle's actual speed, its gearing, or the load on its brakes. Recalibration corrects an instrument.

Where the signal is picked up decides what affects it

Two architectures are in service, and they behave differently under a driveline change.

• Wheel-speed sensors. The signal originates at the hub, downstream of everything. Tire circumference is the only variable; changing the axle ratio has no effect on the reading at all.
• A sensor on the transmission output shaft. The signal originates upstream of the ring and pinion, so the stored constant has to account for the axle ratio as well as the tire. On these vehicles a regear shifts the speedometer, and a regear chosen to restore engine speed after a tire change happens to restore the reading too — the two errors cancel because they are the same ratio in opposite directions.

Which one a given vehicle uses is not guessable from its age. Plenty of vehicles with anti-lock brakes still derive the cluster's speed from the tailshaft, and the wiring diagram or the module's parameter list is the way to tell.

What else reads the same signal

Wheel speed is not consumed by the cluster alone. Anti-lock braking and stability control use it as a reference, adaptive cruise systems use it for closing speed, and automatic transmissions use it for shift scheduling. Correcting the stored constant realigns all of them; correcting the display alone realigns one.

Working out your own numbers

The speedometer error calculator takes an original size and a fitted size and returns the full indicated-versus-actual table. Revolutions per mile explains the quantity being counted, and overall diameter and rolling radius covers why a worn tire drifts back toward the original reading as it loses tread.