Speedometer error: the arithmetic

A speedometer does not measure speed. It counts wheel revolutions and multiplies.

Everything else follows from that one sentence. Whatever multiplier the factory chose was matched to one rolling circumference, and it stays matched to it forever. Put a tire of a different circumference underneath and the whole scale slides by the ratio between the two. No second term. No correction factor. Nothing else participates.

Both circumferences carry a factor of pi, so the pi divides straight out and what remains is a bare ratio of heights:

true speed = needle reading x (fitted diameter / factory diameter)

Which is the whole subject. The formula is not the interesting part; the three ways people consistently misapply it are.

Mistake one: treating the error as a number of mph

Ask someone how far out their speedometer is and they will answer in mph. "About three off." But the error is a percentage, so it grows with speed, and the number they quote is only true at whatever speed they happened to check.

Take a common downsize. A car that left the factory on 225/60R17 — 27.63 in across — fitted with 225/55R17 instead, at 26.74 in. That is 0.89 in shorter, or 3.21%.

Indicated	Actual
30 mph	29.0 mph
60 mph	58.1 mph
70 mph	67.8 mph
80 mph	77.4 mph

One mph out in a car park. Two and a half at motorway speed. Anyone who calibrated their mental correction on a residential street is carrying a figure that is wrong by a factor of two and a half where it matters. Run the pair and the whole curve appears at once.

Note also the direction. This tire is shorter, so the wheel turns more often per mile and the needle reads high — the car is doing less than it claims. Almost every discussion of this subject assumes the opposite case, because most people are going up in size, and the sign flip catches them out.

Mistake two: thinking width is involved

It is not. Not at all.

225/60R17 and 245/55R17 differ by 0.79 in of section width, which is a visible, obvious, photographable difference. Their overall diameters differ by 0.02 in, and the speedometer error between them is 0.07% — less than a tenth of a mile per hour at motorway speed, which is far below the resolution of the instrument you would be reading it on.

The needle cannot see width. It cannot see tread pattern, compound, load range, brand or pressure placard. It sees how many times the wheel went round, and that is governed by one dimension. A wider tire that happens to be the same height changes nothing the cluster can detect.

This is the cleanest illustration of a general point: the two dimensions of a tire own completely different sets of consequences, which is worked through in diameter vs width: which changes what.

Mistake three: assuming the factory reading was correct to begin with

It almost certainly was not, and deliberately so.

Type-approval rules across much of the world forbid a speedometer from ever under-reading, and cap how far it may over-read: no more than a tenth above true, plus a small fixed allowance on top. The speedometer calibration reference states the rule properly.

Treat it as a design brief and the consequence writes itself. No manufacturer can aim the calibration at zero error, because ordinary tread wear would drop half the fleet below the floor within a year. The reading therefore leaves the factory leaning high. Your speedometer was already flattering you before you touched it.

That has a practical implication people find counter-intuitive. A modestly taller tire moves the reading down, toward true — it is cancelling a bias that was engineered in, not introducing one. A shorter tire, like the example above, stacks on top of the factory bias and compounds it.

None of which tells you what your particular vehicle's original error was. That is a measurement, not a calculation: it takes a GPS reference or a measured distance. What the arithmetic gives you is the change, exactly, and the change is the part you caused.

The odometer is the same error, and it does not reset

The odometer is fed by the same pulse count, so it carries the same percentage — and unlike the speedometer, it accumulates.

At 3.21%, every 100 miles the odometer reports are 96.8 miles actually driven. Small enough to ignore for a week. Over a 36,000-mile powertrain warranty it means the instrument reaches 36,000 after roughly 34,850 real miles. You are handing back about 1,150 miles of coverage you paid for and never used.

The same arithmetic runs the other way on a leased vehicle with a mileage allowance, where you are billed on the indicated figure. And it quietly compresses every service interval: an oil change nominally due every 7,500 miles arrives 3.21% earlier in real distance, which over a few years is an extra service you did not need.

Nobody is going to change a tire choice over 3%. But it is worth knowing that the drift is one-directional, that it is exactly computable, and that it never washes out.

What actually fixes it

Two mechanisms, depending on the vehicle's age.

On anything modern, the speed signal originates at a wheel-speed sensor reading a fixed number of teeth per revolution, and the conversion from pulses to mph is a constant in software. Correcting it means changing that constant — either through the manufacturer's own tire-size configuration, where one is offered, or with an aftermarket module that rescales the signal.

On older vehicles the drive is mechanical, taken from the transmission output, and the correction is a physical part: a different-toothed speedometer drive gear. Which also means that on those vehicles, and only those, an axle-ratio change moves the speedometer too — something worth knowing before re-gearing.

What does not fix it is inflation pressure, tread depth, or waiting. Those move the rolling radius by fractions of a percent in the noise; the size change moved it by 3.21% and left it there.

Getting your own number

Three inputs, one output. Your original size, from the vehicle's tire and loading information placard rather than from whatever is currently fitted — those are frequently not the same thing. The size you are considering. That is it.

The speedometer error calculator gives the full indicated- versus-actual table, and the comparison tool puts the same figure next to everything else the change moves. If you want the gap between a calculated height and the height a tire actually rolls on, that is its own subject.

One honest caveat, which applies to every figure above. These are geometric diameters, computed from the size code. A loaded tire is fractionally shorter than a free one, and the deflection differs between two casings. The absolute numbers are therefore approximations. The ratio — which is what speedometer error actually is — survives that almost intact, because the deflection is a similar proportion on both tires and largely divides out.