Vehicle tire circumference:
how far one wheel turn carries you

One turn, one circumference

Each time a wheel completes a full revolution on the road, the vehicle moves forward by the length of the tire's outer edge. That length is the circumference, found from the diameter with the same rule used for any circle.

The diameter must be the overall diameter of the tire mounted on the rim and inflated, not the rim size alone. A common slip is to use the radius, which gives a result half as long; if you have a radius, the circumference is 2 × π × radius.

Getting the diameter from the sidewall code

A tire marked 205/55 R16 contains all you need. The first number is the section width in millimetres. The second is the aspect ratio, the sidewall height as a percentage of the width. The last is the rim diameter in inches.

1. 1Sidewall height = width × aspect ratio = 205 × 0.55 = 112.75 mm.
2. 2Rim diameter in mm = 16 × 25.4 = 406.4 mm.
3. 3Overall diameter = rim + 2 × sidewall = 406.4 + 225.5 = 631.9 mm.
4. 4Circumference = π × 631.9 ≈ 1,985 mm, or 1.985 m.

That is a little under the 0.65 m example, which suggests a slightly taller tire, such as one with a bigger aspect ratio or rim. The method is the same either way.

Why the real figure is a little shorter

The formula assumes a rigid circle. A loaded tire flattens where it meets the road, so the effective rolling radius is a little smaller than half the unmounted diameter, and the distance per turn is a little less than the calculated value. Wear reduces it further as the tread wears down, and a tire at low pressure is smaller still.

For most planning the difference is a percent or so. To get an exact figure, mark the tire and the road, roll the vehicle forward one full revolution and measure the distance, or divide a measured distance by the number of wheel turns counted over a long straight run.

Effect on speedometer and odometer

Speedometers count wheel turns and multiply by the circumference the manufacturer assumed. Fit a tire with a different overall diameter and the reading is off by the ratio of the two sizes. A new tire 3% taller makes the speedometer read about 3% slow, so the real speed is higher than the display.

In the table the 0.650 m tire is about 2.9% larger in diameter than the 0.632 m one. With the speedometer calibrated for the smaller tire, the display at an indicated 100 km/h would correspond to roughly 102.9 km/h on the road.

Other uses of the number

• Odometer correction: scale recorded distance by the ratio of new to old circumference.
• Cycle computers: they need the wheel circumference in millimetres to convert spokes pulses into speed.
• Gearing: wheel circumference and final-drive ratio together decide road speed at a given engine rpm.
• Fleet and agriculture work: checking tire size changes after fitting wider or taller tires.

For the arithmetic of a circle from either a diameter or a radius, a general circle-circumference tool is enough. Input the diameter in metres and read the result in metres, then convert to revolutions per kilometre by dividing 1,000 by the answer.

Using it to check an odometer

Suppose a vehicle's trip meter shows 100 km after a drive, but you suspect the tires were changed to a different size. The meter was calibrated for a 1.985 m circumference and the new tires measure 2.042 m. The meter counts wheel turns, so the true distance is the indicated distance times the ratio of the two circumferences.

A GPS trace of a known route, a mapped highway between two kilometre posts, or a phone navigation app gives an independent reference. Compare it with the odometer over at least 20 km to smooth out small errors, then use the ratio as a correction factor.

Smaller wheels, same method

Bicycle and scooter wheels follow the same rule, but the diameter is measured differently. A bicycle labelled 700c with a 25 mm tire has an overall diameter of roughly 668 mm, which makes a circumference of about 2,099 mm. Cycle computers ask for this value in millimetres, and a wrong entry scales every speed and distance reading by the same percentage.

The most accurate way to set one is the roll-out test: sit on the bike with normal load, roll forward one full wheel revolution on a flat surface, and measure the distance between the valve marks. It captures the effect of tire pressure and rider weight that a formula leaves out.

Common slips

• Mixing units: inches for the rim and millimetres for the width in one expression.
• Forgetting that the sidewall appears twice in the diameter, above and below the rim.
• Using the nominal marked size as if it were exact; manufacturers' actual diameters vary by a few millimetres.
• Using the rolling circumference without allowing for the 1% to 3% difference from the unloaded size when you need accuracy.