Rolling circumference, tachograph error and mixing sizes

Rolling circumference is the distance a tyre actually travels in one revolution, loaded and inflated — not the geometric circumference of the circle. It is smaller than the free circumference because the tyre deflects where it meets the road. Every speedometer, odometer and tachograph reading on a vehicle is derived from it, which is why changing size is never only a fitment question.

Change the circumference and you change what the vehicle reports it did. This affects instrument accuracy and fitment decisions.

Free rolling circumference is measured with the tyre inflated, unloaded and rotating — effectively the outside of the tyre laid flat. You can approximate it from the size: overall diameter times pi. For 315/80R22.5 the rim is 22.5 × 25.4 = 571.5 mm and the section height is 80% of 315 = 252 mm, twice, so the overall diameter is about 1,075 mm and the free circumference about 3,378 mm.

Loaded rolling circumference is the real one: the distance covered per revolution with the axle load on it, at the correct pressure and a reference speed. The tyre flattens in the contact patch, so the effective radius is shorter — typically 96 to 97 per cent of the free figure. On that size it lands around 3,250 mm, close to the figures manufacturers publish.

Both move with pressure, load and speed, which is why the published figure is stated against defined conditions rather than being a property of the tyre alone.

Two tyres of the same nominal size from different patterns do not have the same rolling circumference. Tread depth differs, the tread profile differs, the belt package and casing stiffness differ, and each of those changes the deflected radius by a few millimetres.

So the manufacturer measures it, per pattern and per size, and publishes both the rolling circumference in millimetres and the revolutions per kilometre. The two are the same fact expressed twice: revolutions per kilometre is 1,000,000 divided by the rolling circumference in millimetres. At 3,250 mm that is about 308 revolutions per kilometre.

For tachograph work, use the manufacturer’s published figure for the exact pattern and size fitted. Our calculator estimates from the size for comparison purposes, and is intended for an initial size comparison. It must not be used for calibration certification.

The vehicle counts revolutions and multiplies by a stored constant. If the fitted tyre covers more ground per revolution than the constant assumes, the vehicle under-reads: the speedometer shows less than the true speed and the odometer records fewer kilometres than were driven. Fit something smaller and it over-reads.

The error is simply the percentage difference in circumference. A tyre 2 per cent larger in diameter means a speedometer reading about 2 per cent low — at an indicated 90 km/h the vehicle is doing about 92. Over a year of trunking, a 2 per cent odometer error is thousands of kilometres that never appear in the maintenance schedule or the cost per kilometre figures.

The rule of thumb across the industry is ±3 per cent. Inside that, a substitution is usually treated as acceptable on gearing and instrument grounds; outside it, expect problems with clearance, gearing, driveline speeds and instrument accuracy, and treat it as a specification change rather than a substitution. It is a rule of thumb, not a permission — the vehicle manufacturer’s approved fitment list outranks it.

On a vehicle fitted with a tachograph, tyre size is not a workshop preference. The recording equipment is calibrated to the vehicle: the relationship between the sensor’s pulses and distance travelled depends directly on the effective circumference of the wheel tyres, and that circumference is one of the parameters recorded on the calibration plaque.

Change the size and that parameter is no longer true. The tachograph then records distances and speeds that do not match reality, which affects drivers’ hours and speed records — the evidence, not just the instrument. The requirement is straightforward: a change of tyre size means the vehicle goes to an approved tachograph centre for recalibration and a new plaque, regardless of when the last calibration was done.

Periodic inspection and calibration intervals are set separately by the tachograph rules; confirm the current ones with DVSA or your approved centre using current guidance. It is also why the ±3 per cent rule is not the whole answer here — a 1 per cent change is inside every rule of thumb going and still makes the recorded distance wrong.

Two tyres bolted either side of the same wheel centre are forced to turn at the same speed. If one has a larger rolling circumference, it wants to travel further per revolution and cannot, so the difference comes out as scrub, heat and load transfer.

The larger tyre carries more than its share while the smaller one skips along under-loaded and scrubs. Both run hot. Irregular wear appears on the pair within a few thousand kilometres and the casings are compromised long before the tread is used up.

Keep the diameters of a pair close. Workshop practice is measured in a few millimetres rather than tens, and manufacturers publish their own limit — commonly quoted as no more than around 6 mm difference in overall diameter across a twin. Match pattern, construction and wear state: a new tyre paired with a half-worn one of the same size is still a mismatch. Where a retread goes onto a twin, check its circumference against its partner — see retread or replace.

Across a single driven axle, the differential absorbs a circumference difference between left and right — but it absorbs it by working continuously instead of sitting still. That means constant differential action, extra heat in the axle oil, and accelerated wear in the differential gears.

On a twin-drive bogie with an inter-axle differential, or with a locked or through-drive arrangement, a mismatch between the two axles has nowhere to go at all. The driveline winds up, torque circulates between the axles, and the result is heat and eventually damage — to the axle, not just to the tyres. The same applies to all-wheel-drive plant and to tractors, where front-to-rear ratio is fixed by design and a wrongly sized front tyre puts the transmission in permanent conflict with itself.

Treat matched circumference across driven axles as a hard requirement, not a preference.

More than most people expect. One millimetre of tread depth is 2 mm of overall diameter, which is about 6.3 mm of circumference.

A drive tyre starting at 15 mm and removed at 3 mm has lost 12 mm of depth — 24 mm of diameter, roughly 75 mm of circumference. On a 315/80R22.5 that is about 2.2 per cent, and a change from around 308 to around 315 revolutions per kilometre over its life.

The useful consequence: a new-to-worn swing consumes most of the ±3 per cent budget on its own. Spend the rest of it on a size substitution and the vehicle will be outside the tolerance for the second half of the tyres’ life without anyone changing anything.