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Gear Train Calculator

Enter driver and driven gear teeth counts, input speed, and torque to calculate gear ratios, output RPM, and torque. Choose simple pair, compound train (up to 4 pairs), or planetary epicyclic configuration. The animated SVG shows meshing gear teeth rotating at correct relative speeds.

Simple Gear Pair— Paused

↻↺Driver20 teeth1200 RPMDriven40 teeth600 RPMRatio 2:1 — reverse direction
DriverDriven
Driver teeth20
Driven teeth40
Input RPM1200
Input torque (N·m)10
Efficiency98%

Results

Gear Ratio=NdrivenNdriver=4020=2.0000\text{Gear Ratio} = \frac{N_{\text{driven}}}{N_{\text{driver}}} = \frac{40}{20} = 2.0000
Gear ratio
2:1
Direction
Reverse
Output RPM
600.0
RPM
Output torque
19.600
N·m
Speed ratio
0.5000
(output/input)
Efficiency
98%
Driver diameter
40
mm (m=2)
Driven diameter
80
mm (m=2)
Nout=12002.00=600.0 RPMN_{\text{out}} = \frac{1200}{2.00} = 600.0\,\text{RPM}
τout=10.0×2.00×0.98=19.600 N⋅m\tau_{\text{out}} = 10.0 \times 2.00 \times 0.98 = 19.600\,\text{N}\cdot\text{m}

Reference Guide

Gear Basics

A gear is a toothed wheel that meshes with another gear to transmit rotational motion. Gear teeth interlock so that no slipping occurs, making gears more reliable than belt drives for precise timing applications.

Key parameters

  • Teeth count (N) — number of teeth on the gear
  • Module (m) — tooth size; pitch diameter = m × N
  • Pitch diameter (d) — reference diameter for mesh calculations
  • RPM — rotational speed in revolutions per minute

When two external gears mesh, they rotate in opposite directions. Adding an idler gear between them reverses the output direction back to the same as the input.

Gear Ratios

The gear ratio equals the number of driven teeth divided by the number of driver teeth. A ratio greater than 1 means speed reduction and torque multiplication.

Gear ratio
R=NdrivenNdriverR = \frac{N_{\text{driven}}}{N_{\text{driver}}}
Output speed
ωout=ωinR\omega_{\text{out}} = \frac{\omega_{\text{in}}}{R}
Output torque (ideal)
τout=τin×R×η\tau_{\text{out}} = \tau_{\text{in}} \times R \times \eta

Typical spur gear efficiency is 96 to 99%. Real torque output is slightly less due to friction at the tooth mesh and bearing losses.

Compound Gear Trains

A compound gear train has two or more gear pairs in series. Each pair's driven gear shares a shaft with the next pair's driver gear. The overall ratio is the product of all individual ratios.

Overall ratio
Rtotal=R1×R2×⋯×RnR_{\text{total}} = R_1 \times R_2 \times \cdots \times R_n

Example: two pairs each with a 2:1 ratio gives an overall 4:1 ratio. Three pairs of 2:1 gives 8:1. Compound trains can achieve large ratios (10:1 to 100:1) in a compact space.

Direction rule — an even number of external gear meshes produces the same output direction as the input; an odd number reverses it.

Planetary Gear Systems

A planetary (epicyclic) gear set has a central sun gear, one or more planet gears orbiting it, and an outer ring gear with internal teeth. The carrier holds the planet shafts.

Mesh condition

Nring=Nsun+2×NplanetN_{\text{ring}} = N_{\text{sun}} + 2 \times N_{\text{planet}}

By fixing different elements, three distinct ratios are possible from the same gear set. When the ring is fixed and the sun drives, the carrier output speed is:

ωcarrier=ωsun1+Nring/Nsun\omega_{\text{carrier}} = \frac{\omega_{\text{sun}}}{1 + N_{\text{ring}}/N_{\text{sun}}}

Planetary gears are used in automatic transmissions, epicyclic gearboxes, and robot joints because they offer high ratios in a compact, coaxial arrangement with load shared across multiple planet teeth.