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Gear Ratio Calculator

Find the gear ratio, output speed, and output torque for any gear train. Enter driver and driven teeth for up to three stages. See total ratio and mechanical advantage live.

Inputs

Results

Total Gear Ratio
1:1
Output RPM 0 RPM
Output Torque 0 lb-in
Output Torque (lb-ft) 0 lb-ft
Overall Efficiency 0%
Input Power 0 HP
Output Power 0 HP
Formulas used:
Ratio = Ndriven / Ndriver
RPMout = RPMin / Ratio
Tout = Tin × Ratio × Efficiency
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Uses Lame's thick-wall cylinder equations. Verify critical designs with FEA.

How Gear Ratios Work

A gear ratio trades speed for torque. When a small gear drives a big gear, the big gear turns slower but with more force. When a big gear drives a small gear, the small gear turns faster but with less force. The amount of this trade is the gear ratio.

Single Stage vs Multi-Stage

A single gear pair can reduce speed by up to about 10:1 before the gears get awkward in size. For bigger reductions use multiple stages. Three stages at 4:1 each gives a total of 64:1 in a compact package.

Counting Teeth

The ratio is just the number of teeth on the driven gear divided by the driver. A 45-tooth gear driven by a 15-tooth gear has a 3:1 ratio. The output turns one time for every three input turns. Output torque is three times the input torque.

Pro tip: Always use at least 12 to 14 teeth on the smallest gear to avoid undercutting. Fewer teeth causes contact problems and reduces tooth strength.

Efficiency Losses

Real gears lose a few percent of power to friction. Spur gears are 97 to 98 percent efficient per stage. Helical gears are similar. Worm gears can be as low as 50 percent for high reductions. Multiply the efficiency of each stage to get the overall number.

RPM and Torque

Output RPM equals input RPM divided by the ratio. Output torque equals input torque multiplied by the ratio and then by the efficiency. Power is speed times torque, so power stays about the same (minus losses) across the whole train.

Frequently Asked Questions

Gear ratio is the number of driver teeth divided by the number of driven teeth, or it can be expressed as driven over driver. A ratio of 3:1 means the driver turns three times for every one turn of the driven gear. Ratios above 1:1 reduce speed and multiply torque. Below 1:1 they do the opposite.
Output RPM equals input RPM divided by the gear ratio. If your motor runs at 1800 RPM and the gear ratio is 3:1, the output is 600 RPM. For multi-stage gear trains, multiply all the ratios together then divide.
Output torque equals input torque multiplied by the gear ratio, minus losses. A 3:1 reduction triples the torque if the gears are 100 percent efficient. Real gears are 95 to 98 percent efficient per stage, so a 3-stage train might be 90 percent overall.
Mechanical advantage is the output force divided by the input force. For gears it is the same as the gear ratio. A gear train with 10:1 reduction gives you ten times the torque at the output, at the cost of one-tenth the speed.
A multi-stage gear train combines ratios. If stage one is 3:1 and stage two is 4:1, the total ratio is 12:1. Multi-stage lets you get high reductions with small individual gears. Industrial gearboxes often use 3 or 4 stages.
Planetary gears have three elements: sun, ring, and carrier. The ratio depends on which element is the input, output, and fixed. This calculator covers parallel shaft gear trains (spur, helical, bevel). For planetaries, use a dedicated calculator.
Efficiency is how much input power gets to the output. Spur gears are about 98 percent efficient per stage. Worm gears can be as low as 50 percent. This calculator assumes 100 percent for the theoretical ratio. For real output torque multiply by the efficiency of each stage.
Yes. For gears with the same diametral pitch or module, the ratio of the pitch diameters equals the ratio of the teeth. If you know the pitch diameters, use those. If you know the outside diameters, they are close but not exact.
A reduction ratio like 3:1 cuts output speed to one-third of input. An overdrive ratio like 1:3 triples the output speed. Car transmissions use different ratios in each gear to match engine RPM to wheel speed.
An idler gear does not change the ratio between the driver and the final driven gear. It only changes the direction of rotation. Some gear trains use idlers to reach a specific direction or shaft spacing without affecting the ratio.

Typical Gear Reduction Stages

Gear Type Max Ratio per Stage Efficiency per Stage Common Use
Spur Gears6:196-98%Parallel shafts, simple drives
Helical Gears8:196-98%Smoother, higher loads
Bevel Gears5:193-97%90-degree shaft angles
Worm Gear60:140-90%High reduction, compact
Planetary (single)10:197-98%Concentric shafts, high torque
Harmonic Drive320:150-75%Robotics, precision positioning
Cycloidal200:185-95%Shock-tolerant, backlash-free

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