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Gear Ratio Calculator

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Enter the tooth count of two meshing gears to find the gear ratio, and how it changes output speed and torque relative to the input.

Gear Ratio Calculator

Live
Gear ratio
3:1
Output RPM
1,000
Torque multiplier
3.0x
Ignores friction losses - real-world efficiency is always somewhat below 100%.

The formula

Gear ratio = Driven teeth / Driver teeth Output RPM = Input RPM / Gear ratio Output torque = Input torque x Gear ratio
Example

A 20-tooth driver gear turning a 60-tooth driven gear: ratio = 60/20 = 3:1. At 3,000 input RPM, the output shaft spins at 1,000 RPM but with 3x the input torque.

Step-by-step guide

  1. Enter the tooth count of the driver gear - the one connected to the input power source.
  2. Enter the tooth count of the driven gear - the one connected to the output.
  3. Optionally enter input RPM to see the resulting output RPM.

The fundamental speed-torque tradeoff

Gears don't create energy - they trade speed for torque, or torque for speed, in exact proportion. A ratio above 1:1 (driven gear larger than driver) reduces output speed while multiplying torque, common in situations needing high force at low speed. A ratio below 1:1 does the opposite - increasing speed while reducing torque, common when a small, fast-spinning motor needs to drive something requiring higher speed than torque.

Common mistakes

Mixing up which gear is the driver and which is driven - swapping them inverts the entire ratio and gives the exact opposite speed/torque result.
Forgetting friction and mechanical losses - a real gear train never achieves the full theoretical torque multiplication, since some energy is lost to friction, especially in multi-stage systems.

Frequently asked questions

Does the direction of rotation change between driver and driven gears?

Yes, for two gears meshing directly - the driven gear spins opposite to the driver. Adding a third idler gear between them reverses direction back to match the driver without changing the overall ratio.

How does this extend to a multi-stage gear train?

Multiply the individual ratios of each stage together to get the overall ratio - a 3:1 first stage feeding into a 2:1 second stage gives a combined 6:1 ratio.

Does gear ratio apply to belt and pulley systems too?

Yes - the same principle applies using pulley diameters instead of tooth counts, since the ratio of circumferences determines the speed and torque relationship the same way tooth count does for gears.

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