How this calculator works
A mechanical speedometer is driven by a gear pair from the transmission output shaft. The drive gear turns with the output shaft and the driven gear turns the cable. The speedometer is calibrated for a fixed number of cable revolutions per mile. Wheel revolutions per mile come from the tire diameter, and the axle ratio multiplies them to give output shaft revolutions. The driven tooth count needed is therefore the driving tooth count times the axle ratio times the wheel revolutions per mile, divided by the speedometer calibration. Only whole tooth counts exist, so the page also shows the nearest available gear and the resulting error.
Formula
wheel revolutions per mile = 1,609.344 / (pi x tire diameter). Driven teeth = driving teeth x axle ratio x wheel revolutions per mile / calibration. Driving teeth = driven teeth x calibration / (axle ratio x wheel revolutions per mile).
Worked example
A 700 mm tire turns 731.9 times per mile. With a 3.73 axle and 20 driving teeth at a 1,000 revolution per mile speedometer, the exact driven tooth count is 20 x 3.73 x 731.9 / 1000 = 54.60. A 55 tooth gear is the nearest available, and it makes the speedometer read about 0.73 percent low.
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Frequently asked questions
Does a different tire size change the gear I need?
Yes. A larger tire turns fewer times per mile, so it needs a driven gear with fewer teeth, or a driving gear with more teeth, to keep the speedometer accurate.
Why is the error negative or positive?
A positive error means the speedometer reads high with the nearest gear; a negative error means it reads low. The magnitude is the percentage difference from the exact tooth count.
How accurate is the 1,000 revolutions per mile figure?
It is common for North American speedometers but not universal. Check the specification for your instrument, and use the calibration printed for your vehicle if you have it.
Is this for a cable speedometer or a sensor?
The tooth-count arithmetic applies to both mechanical gear sets and pulse-based sensors that emulate a gear ratio. For a pure pulse sensor, use the pulses per mile calculator instead.