Hong Life CalculatorsUnderstanding the speedometer gear calculator — concept and principle
A mechanical speedometer counts turns of the transmission output shaft. When you change the axle ratio or fit taller or shorter tyres, the shaft turns a different number of times per kilometre and the speedometer goes wrong. This calculator finds the driven-gear tooth count that restores the original calibration, rounds it to a real gear and shows the error that remains.
How it is calculated
Ideal teeth = old teeth × (new axle ratio ÷ old axle ratio) × (old tyre diameter ÷ new tyre diameter)
Error with nearest gear (%) = (nearest ÷ ideal − 1) × 100
Reading at a true 100 = 100 × nearest ÷ ideal
- The axle (final drive) ratio says how many times the driveshaft turns per wheel turn.
- Tyre diameters can be in inches or millimetres, as long as both use the same unit.
- The error if the gear is not changed uses the old tooth count instead of the nearest one.
The principle
For a fixed road speed, the wheel turns once per tyre circumference, so wheel rpm is inversely proportional to tyre diameter. The output shaft turns axle-ratio times faster than the wheel. A numerically higher axle ratio therefore spins the shaft faster, and a bigger tyre spins it slower. The speedometer cable must keep the same speed per kilometre as before, so the driven gear must grow or shrink by exactly the same factors. Because a gear has whole teeth, the nearest available count leaves a small residual error. A positive error means the speedometer reads high.
Worked example
Default inputs: 20-tooth driven gear, axle ratio 3.73 → 4.10, tyre 28 → 31 in.
- Axle factor = 4.10 ÷ 3.73 = 1.0992.
- Tyre factor = 28 ÷ 31 = 0.9032.
- Ideal teeth = 20 × 1.0992 × 0.9032 = 19.86.
- Nearest whole tooth count = 20.
- Error = (20 ÷ 19.86 − 1) × 100 = 0.7 %. Since the nearest gear is the current one, the error without a change is also 0.7 %.
- At a true 100, the speedometer shows 100.7.
| Old axle (final drive) ratio | Ideal driven-gear teeth |
|---|---|
| 0.932 | 79.43 |
| 1.86 | 39.71 |
| 2.8 | 26.48 |
| 3.73 | 19.86 |
| 4.66 | 15.89 |
| 5.59 | 13.24 |
| 7.46 | 9.93 |
How to read the result
Errors below about 1 % are generally hard to notice. If the error is large, check whether a different drive gear is available as well, because changing both gears gives more combinations. In this example the bigger tyres almost cancel the steeper axle ratio, so the original gear still works. A positive error reads high (safer for speed limits), a negative error reads low.
Common mistakes
- Using nominal tyre sizes instead of measured or calculated overall diameters.
- Mixing inches for one tyre and millimetres for the other.
Frequently asked questions
Does a bigger tyre make the speedometer read high or low?
Low. The wheel turns fewer times per kilometre, so the speedometer under-reads unless the gear is changed.
Why is the result rarely a whole number?
The ratios are decimals, so the ideal tooth count usually falls between two real gears.
Does this also correct the odometer?
On a mechanical system the odometer is driven by the same cable, so correcting the gear fixes both.
Sources: Standard gear-train kinematics (speed ratios of meshing gears and wheel rotation per distance)