Which speedometer gear do I need?

The one whose tooth count is closest to the ideal, and the ideal is drive teeth × axle ratio × tire revolutions per mile ÷ the speedometer's calibration. With an 8 tooth drive gear, a 3.55 axle, a 26 inch tire and a 1,000 revolution speedometer, that comes to 22.03 teeth, so a 22 tooth gear is the one to order. The leftover fraction is the error you live with, and picking the neighbouring tooth count moves it to the other side.

Which way does the error go?

Too few teeth makes the cable spin faster than it should, so the speedometer reads high. Too many teeth makes it read low. Reading high is the dangerous direction — the car is going slower than the needle says, and every speed limit you think you are obeying is one you are exceeding. When the ideal count sits halfway between two gears, take the one with more teeth.

What is the difference between a 1000 and an 820 speedometer?

The calibration: how many times the cable must turn for one mile. Most American speedometers are 1,000, a group of GM and Japanese cars are 820, and an aftermarket gauge can be anything. The number changes the answer substantially — 28 inch tires, a 3.73 axle and an 8 tooth drive gear want 26 teeth at 820, but 21 teeth at 1,000. Check the calibration before ordering a gear.

Does the tire diameter have to be exact?

It should be the rolling diameter, which is smaller than the number on the sidewall. A 33 inch tire measures about 33 inches across when it is off the car, but flattened under load it rolls as if it were 1–3% smaller, and that goes straight into the tooth count. Measure with the car on the ground if you can. The difference between a new tire and a worn one is a few tenths of a percent, which is below the resolution of the tooth counts on sale.

Can I use this on an electronic speedometer?

No. An electronic speedometer counts pulses from a speed sensor on the transmission or a wheel, and there is no gear pair to change. Tire and axle changes are corrected by reprogramming the value the instrument uses — with a dealer tool, a tuning device, or an inline correction module. The arithmetic on this page is the same arithmetic that has to happen, but you cannot buy the answer as a gear.

Speedometer Gear Calculator

Result

Driven gear teeth to fit

Ideal tooth count: 22.03
Speedometer error after fitting: 0.14%
Tire revolutions per mile: 775.7 rev/mi

A mechanical speedometer is driven by a small gear on the transmission output shaft and a driven gear on the end of the cable, and its calibration is fixed: the cable turns a set number of revolutions per mile, usually 1,000. Change the tire diameter or the axle ratio and that relationship breaks. This speedometer gear calculator works out the driven gear tooth count that puts it back — the ideal count, the whole number of teeth closest to it, and the speedometer error that remains once the nearest gear you can actually buy is fitted. On a 26 inch tire with a 3.55 axle and an 8 tooth drive gear, the ideal is 22.03 teeth, so the 22 tooth gear leaves an error of 0.14%, which is as close to correct as a geared speedometer ever gets. Fit a taller 33 inch tire with a 4.56 axle and the ideal drops to 22.29 against the same 22 tooth gear, an error of 1.34% — still small, but on the wrong side. A speedometer reading high is the side that gets you a ticket, so the direction of the error is as important as its size.

Tire diameter and revolutions per mile

Tire size	Nominal diameter (in)	Revolutions per mile
205/55R16	24.9	811
215/60R16	26.2	771
225/45R17	25	808
225/60R16	26.6	757
235/40R18	25.4	794
235/75R15	28.9	698
245/45R18	26.7	756
265/35R18	25.3	797
275/40R17	25.7	786
275/60R15	28	720
31x10.5R15	31	651
33x10.5R15	33	611

The diameter is geometry, not a measurement: rim diameter plus twice the sidewall height, where the sidewall is the section width multiplied by the aspect ratio. Two rows at the bottom are light truck sizes, which state their diameter directly. The revolutions per mile column follows from that diameter and is therefore a slight overestimate of the real figure — a tire flattened under load rolls on a smaller radius, so the true count is 1–3% higher, and the speedometer error that comes out of this page is optimistic by about that much.

Formula

driven teeth = drive teeth × axle ratio × tire revolutions per mile ÷ speedometer calibration

tireDiameter: Overall tire diameter, in inches
axleRatio: Axle or final drive ratio
driveGearTeeth: Teeth on the drive gear in the transmission
speedoRevsPerMile: Speedometer calibration, in cable revolutions per mile

Use it after fitting a different tire size or a different axle ratio, or when a speedometer has been reading wrong since you bought the car and you want to know whether the gear is the reason. It also answers the reverse question without any extra work: put today's gear in the drive gear field and the result tells you how many teeth that gear was sized for, which is how you find out whether a previous owner already swapped it.

Worked examples

A 26 inch tire, 3.55 axle, 8 tooth drive gear, 1000 revolutions per mile
1. Circumference: π × 26 in = 81.68 in, so the tire turns 63,360 ÷ 81.68 = 775.7 times per mile
2. The transmission output shaft turns 3.55 times per wheel revolution, through the axle ratio: 775.7 × 3.55 = 2,753.7 turns per mile
3. The 8 tooth drive gear sits on that shaft, so it presents 2,753.7 × 8 = 22,030 teeth per mile
4. The speedometer expects the cable to turn 1,000 times per mile, so it can spend 22,030 ÷ 1,000 = 22.03 teeth on each of those revolutions
5. 22.03 is the ideal tooth count, and the nearest gear on sale has 22 teeth
6. Error with 22 teeth: 22.03 ÷ 22 − 1 = +0.14%, reading slightly high
22.03 teeth is the answer to a question nobody can act on, which is why the primary output is the 22 tooth gear you can order. The 0.14% left over is the reason a geared speedometer is never exact: the tooth count is an integer and the ideal one almost never is. It is also why the error can be pushed either way — a 21 tooth gear would leave +4.9% and a 23 tooth gear −4.2% — so the gear either side of the ideal is always worth pricing before ordering.
An 820 revolution speedometer with a taller tire, 28 inch and 3.73
1. Circumference: π × 28 in = 87.96 in, so 63,360 ÷ 87.96 = 720.3 revolutions per mile
2. Output shaft turns per mile: 720.3 × 3.73 = 2,686.7
3. Teeth presented per mile: 2,686.7 × 8 = 21,494
4. This speedometer wants 820 cable revolutions per mile, so each one may spend 21,494 ÷ 820 = 26.21 teeth
5. The nearest gear is 26 teeth
6. Error with 26 teeth: 26.21 ÷ 26 − 1 = +0.81%, reading high
The calibration is an input, not a constant. This car's speedometer is built for 820 cable revolutions per mile rather than 1,000, and the same inputs under a 1,000 calibration would want 21 teeth instead of 26. Hard-coding 1,000 would put a gear in this car that is 22% out, so the first thing to check on an unfamiliar car is which calibration its speedometer uses.
A 33 inch tire with a 4.56 axle
1. Circumference: π × 33 in = 103.67 in, so 63,360 ÷ 103.67 = 611.2 revolutions per mile
2. Output shaft turns per mile: 611.2 × 4.56 = 2,787.1
3. Teeth presented per mile: 2,787.1 × 8 = 22,297
4. At a 1,000 revolution calibration: 22,297 ÷ 1,000 = 22.29 teeth ideal
5. 22 teeth is the nearest gear
6. Error with 22 teeth: 22.29 ÷ 22 − 1 = +1.34%, reading high
A much taller tire and a much shorter axle, and the ideal tooth count barely moves — 22.29 against 22.03 in the first example. That is not a coincidence: the taller tire lowers the cable speed and the shorter axle raises it, and here the two nearly cancel. It is also why the answer to "I lifted my truck" is often that the speedometer was already close and the 22 tooth gear still fits.

Limitations

This is for mechanical speedometers driven by a gear pair and a cable. Most cars built since the 1990s have an electronic speedometer fed by a vehicle speed sensor, and there is no gear to change — the correction is made in software, by a dealer tool, a tuner, or a calibration box. Fitting a ratio adapter or an inline corrector is the usual answer there, and this page's tooth counts do not apply. The tire diameter must be the true rolling diameter rather than the nominal one: a tire flattened under load rolls on a radius 1–3% smaller than its geometric half-height, and that error goes straight into the answer, which is why a car with a brand new set of tires reads slightly differently from the same car with worn ones. The tooth counts available are whatever the aftermarket sells — usually 17 to 45 in single steps, sometimes only a few sizes — and a count that this page suggests may simply not exist for your transmission. Chevrolet, Ford and Chrysler use different drive gears and different housing sizes, so the number is not the whole story when you order the part.

Frequently asked questions

Which speedometer gear do I need?: The one whose tooth count is closest to the ideal, and the ideal is drive teeth × axle ratio × tire revolutions per mile ÷ the speedometer's calibration. With an 8 tooth drive gear, a 3.55 axle, a 26 inch tire and a 1,000 revolution speedometer, that comes to 22.03 teeth, so a 22 tooth gear is the one to order. The leftover fraction is the error you live with, and picking the neighbouring tooth count moves it to the other side.
Which way does the error go?: Too few teeth makes the cable spin faster than it should, so the speedometer reads high. Too many teeth makes it read low. Reading high is the dangerous direction — the car is going slower than the needle says, and every speed limit you think you are obeying is one you are exceeding. When the ideal count sits halfway between two gears, take the one with more teeth.
What is the difference between a 1000 and an 820 speedometer?: The calibration: how many times the cable must turn for one mile. Most American speedometers are 1,000, a group of GM and Japanese cars are 820, and an aftermarket gauge can be anything. The number changes the answer substantially — 28 inch tires, a 3.73 axle and an 8 tooth drive gear want 26 teeth at 820, but 21 teeth at 1,000. Check the calibration before ordering a gear.
Does the tire diameter have to be exact?: It should be the rolling diameter, which is smaller than the number on the sidewall. A 33 inch tire measures about 33 inches across when it is off the car, but flattened under load it rolls as if it were 1–3% smaller, and that goes straight into the tooth count. Measure with the car on the ground if you can. The difference between a new tire and a worn one is a few tenths of a percent, which is below the resolution of the tooth counts on sale.
Can I use this on an electronic speedometer?: No. An electronic speedometer counts pulses from a speed sensor on the transmission or a wheel, and there is no gear pair to change. Tire and axle changes are corrected by reprogramming the value the instrument uses — with a dealer tool, a tuning device, or an inline correction module. The arithmetic on this page is the same arithmetic that has to happen, but you cannot buy the answer as a gear.

References

NIST Guide to the SI, Special Publication 811 — US National Institute of Standards and Technology
The International System of Units (SI Brochure) — Bureau International des Poids et Mesures

Related calculators

Gear Ratio CalculatorGear ratio and output speed from tooth counts.Wheel Offset CalculatorWheel offset and backspacing changes from a new rim.Speed Distance Time CalculatorSolve for speed, distance or time from the other two.Engine Displacement CalculatorEngine displacement from bore, stroke and cylinders.