How do you calculate the speed of a driven gear?

Multiply the driver’s speed by its number of teeth, then divide by the driven gear’s teeth: driven rpm = driver rpm × driver teeth ÷ driven teeth. A 20-tooth gear at 60 rpm turns a 40-tooth gear at 30 rpm.

Which way does the last gear turn?

Each pair of meshed gears reverses direction. With two gears the driven gear turns opposite to the driver; one idler between them makes it turn the same way; two idlers reverse it again. An odd number of gears in a line means the first and last turn the same way.

Does an idler gear change the gear ratio?

No. An idler’s teeth cancel out in the calculation, so only the first and last gears set the overall ratio. An idler changes the direction of rotation and the spacing between shafts.

Free tool · OAR Mechanical Comprehension

Gear ratio calculator

Enter the teeth on each gear and the driver’s speed to get the driven gear’s rpm, the gear ratio, the change in torque and which way it turns.

Result

Driven gear speed: 30 rpm
Gear ratio (driven : driver): 2 : 1
Output torque: × 2
Direction of the driven gear: Opposite to the driver

The driven gear turns slower than the driver with more torque: speed and torque always trade off.

How the calculation works

Where two gears mesh, their teeth pass the contact point at the same rate. So for every gear in a train, teeth × rpm is the same number:

Driven speed = driver rpm × driver teeth ÷ driven teeth
Gear ratio = driven teeth ÷ driver teeth. Above 1, the output turns slower with more torque; below 1, faster with less.
Direction: each mesh reverses rotation, so two gears turn opposite ways and an idler in between makes them match.

Example: a 20-tooth driver at 60 rpm meshed with a 40-tooth gear: 60 × 20 ÷ 40 = 30 rpm, a ratio of 2 : 1, turning the opposite way. Reverse it, with a 20-tooth driver at 90 rpm, one idler and a 12-tooth output: 90 × 20 ÷ 12 =150 rpm, turning the same way as the driver.

Why speed and torque trade off

An ideal gear train passes power through unchanged. If the output turns twice as slowly, it must turn with twice the torque; if it turns faster, it has less turning force. It is the same trade as every simple machine: you gain force by giving up distance (or speed), or the other way around.

Test yourself: an OAR-style question

A gear train that increases output speed will generally:

Increase the output torque
Keep the torque the same
Decrease the output torque
Stop the gears

Show answer

C. Decrease the output torque

Speed and torque trade off: if the output gear turns faster than the input, it turns with less torque, and the other way around.

Questions like this come up on the Mechanical Comprehension section of the OAR. The 2,604 questions in the app each come with a written explanation.

FAQ

How do you calculate the speed of a driven gear?: Multiply the driver’s speed by its number of teeth, then divide by the driven gear’s teeth: driven rpm = driver rpm × driver teeth ÷ driven teeth. A 20-tooth gear at 60 rpm turns a 40-tooth gear at 30 rpm.
Which way does the last gear turn?: Each pair of meshed gears reverses direction. With two gears the driven gear turns opposite to the driver; one idler between them makes it turn the same way; two idlers reverse it again. An odd number of gears in a line means the first and last turn the same way.
Does an idler gear change the gear ratio?: No. An idler’s teeth cancel out in the calculation, so only the first and last gears set the overall ratio. An idler changes the direction of rotation and the spacing between shafts.

Sources

Checked against these sources on October 24, 2026. Ideal gears: no slipping and no friction losses. For OAR preparation only; not affiliated with or endorsed by the U.S. Navy. Calculations run in your browser.