Gear Ratio, Torque & Speed Generator

Find the gear ratio, output speed, output torque, and power for a pair of meshing gears.

Gear on the input shaft
Gear on the output shaft
Use 100 for the ideal case. A well-made spur gear pair is roughly 95 to 99.
Gear ratio (driven ÷ driver)
Output speed
Output torque
Input power
Output power

How it works

A gear pair trades speed for torque. The tooth counts set the ratio, and the same ratio scales speed down and torque up, or the reverse.

Gear ratio: i = N2 / N1
Output speed: nout = nin / i
Output torque: Tout = Tin × i × η
Power: P = T × 2π × n / 60, with T in N·m, n in RPM, and P in watts

Here N1 is the driver tooth count, N2 is the driven tooth count, and η is efficiency as a decimal, so 97% is 0.97.

Worked example

A 20-tooth pinion drives a 60-tooth gear at 1,200 RPM with 2 N·m of input torque. The ratio is 60 / 20 = 3, so the output speed is 1,200 / 3 = 400 RPM. With no losses, the output torque is 2 × 3 = 6 N·m. At 97% efficiency it drops to 2 × 3 × 0.97 = 5.82 N·m. Input power is about 251 W either way, and the output power is that figure times the efficiency.

Things to know

Reduction or increase. A driven gear with more teeth than the driver slows the output and multiplies torque. A driven gear with fewer teeth speeds the output up and reduces torque.

Rotation direction. A single external gear pair reverses direction. An idler gear between them flips it back without changing the ratio.

Matching gears. Gears only mesh if they share the same module or pitch. When tooth counts aren't known, the ratio also equals the pitch diameter of the driven gear divided by the pitch diameter of the driver.

Efficiency. Real gears lose some power to friction. A well-made spur pair is roughly 95 to 99 percent efficient, and worm gears are typically much lower.

Common questions

Is a higher gear ratio better?

It depends on what you need. A higher ratio gives more torque and less speed at the output. Choose the ratio from the speed and torque your load requires.

Can I use diameters instead of tooth counts?

Yes. For meshing gears, the ratio equals the driven pitch diameter divided by the driver pitch diameter. Tooth counts are more exact, so use them when you have them.

How do I calculate a gear train with more than two gears?

Work stage by stage. Each meshing pair has its own ratio, and the total ratio is the product of the stage ratios. Idler gears in between don't change the total. Multiply the stage efficiencies together as well.

Sources

  • Oberg, E., et al., Machinery’s Handbook, Industrial Press (gearing, gear trains and speed ratios).
  • Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill (gear trains and their ratios).
  • KHK Stock Gears, Gear Technical Reference (module, tooth counts and speed ratio).

Last reviewed: October 8, 2026