Planetary Gear Ratio Calculator

Inputs

View results
Teeth on the central sun gear.
Internal teeth on the ring (annulus) gear. Must exceed the sun, and R − S must be even.
Which member is held stationary — this sets the ratio (Willis equation).
Speed of the driving member.
rpm

Results

Default result
Edit inputs
Gear ratio(i)
4
Pass

4.00:1 reduction — same direction.

Input ÷ output speed (n:1).

Also computed

Planet teeth(P)24

(R − S)/2

Output speed(n₂)750rpm

Method notes 2 notes
  • Ratio from the Willis equation: ring fixed → 1 + R/S; sun fixed → 1 + S/R; carrier fixed → −R/S (output reverses). Output speed = input ÷ ratio.
  • The planet count does not change the ratio — only the sun and ring teeth do. The planets must satisfy R = S + 2P and the set must be assemblable.

Powered by MachineCalcs ↗