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Gear Ratio Calculator

Calculate gear ratios, output speed, and torque for simple and compound gear trains. Enter gear teeth counts or specify desired output parameters.

Gear Ratio = Driven Teeth / Driving Teeth

Calculate the gear ratio for a single meshing gear pair

RPM
N·m
Result:
Total Ratio = (Driven₁/Driving₁) × (Driven₂/Driving₂) × ...

Calculate the overall ratio for a multi-stage gear train

Stage 1
Stage 2
RPM
N·m
Result:
Output Speed = Input Speed / Ratio  |  Output Torque = Input Torque × Ratio

Given a gear ratio, calculate output speed or torque

: 1
RPM
N·m
%
Typical: spur 95–98%, worm 40–90%
Result:

How It Works

What is a Gear Ratio?

A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. It determines how speed and torque are transmitted between meshing gears. A ratio greater than 1:1 means speed reduction and torque multiplication; less than 1:1 means speed increase and torque reduction.

Key Formulas

  • Gear Ratio = Driven Teeth / Driving Teeth
  • Output Speed = Input Speed / Gear Ratio
  • Output Torque = Input Torque × Gear Ratio × Efficiency
  • Compound Ratio = Stage₁ Ratio × Stage₂ Ratio × ... × Stageₙ Ratio

Speed vs. Torque Trade-off

Gears obey conservation of power (minus friction losses). When a gear train reduces speed, it proportionally increases torque, and vice versa. This is the fundamental principle behind transmissions in vehicles, industrial machinery, and robotics.

Types of Gear Arrangements

  • Simple pair: Two meshing gears. The most basic configuration for speed/torque change.
  • Compound train: Multiple stages where an intermediate shaft carries both a driven gear from one stage and a driving gear for the next. Ratios multiply together.
  • Idler gear: An intermediate gear that reverses direction without changing the overall ratio.
  • Planetary (epicyclic): Sun, planet, and ring gears in a compact arrangement for high ratios.

Practical Examples

  • A 20-tooth gear driving a 60-tooth gear gives a 3:1 ratio — output spins 3× slower with 3× more torque
  • A bicycle's low gear (large rear sprocket) gives a high ratio for climbing hills with more force
  • Car transmissions use multiple gear ratios: 1st gear (~3.5:1) for acceleration, 5th gear (~0.8:1) for highway cruising
  • A two-stage compound train with 2:1 and 3:1 stages produces a total 6:1 reduction

Efficiency

Real gear systems lose some power to friction. Typical efficiencies per stage: spur gears 95–98%, helical gears 96–99%, bevel gears 95–97%, worm gears 40–90% depending on lead angle. For compound trains, multiply the efficiencies of each stage.

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