planetary gear ratio calculator

Calculate output speed, ratio, direction, and ideal torque multiplication for a simple planetary gear set (sun, ring, carrier).

Sun gear teeth (Z_s)

Ring gear teeth (Z_r)

Planet gear teeth (optional, geometry check)

For standard geometry: Zr = Zs + 2×Zp

Fixed member (held stationary)

Input member (driven)

Input speed (RPM)

How this planetary gear ratio calculator works

A planetary gear train has three main members: a sun gear, an internal ring gear, and a planet carrier. Any one member can be fixed, one can be used as the input, and the remaining member becomes the output. This is what makes planetary drives compact and extremely versatile for reducers, overdrives, and automatic transmissions.

This calculator uses the classic kinematic relationship for a simple planetary set:

(ωs - ωc) / (ωr - ωc) = -Zr / Zs

Equivalent linear form:

Zs·ωs + Zr·ωr - (Zs + Zr)·ωc = 0

What you can calculate

Output member (automatically determined from your fixed + input selections)
Output speed (RPM)
Speed ratio as input/output
Direction (same or opposite)
Ideal torque multiplication (ignoring losses)
Basic geometry check if planet teeth are provided

Common planetary gear ratio formulas

1) Ring fixed, sun input, carrier output (most common reducer)

i = ωin/ωout = 1 + Zr/Zs

Output rotates in the same direction and usually slower than input.

2) Sun fixed, ring input, carrier output

i = 1 + Zs/Zr

Also a reduction, usually smaller than case 1 for the same tooth counts.

3) Carrier fixed, sun input, ring output

ωout/ωin = -Zs/Zr (direction reverses)

This behaves like a simple gear pair with reversal.

Design notes and best practices

In many standard designs, ring teeth are greater than sun teeth, and planet teeth satisfy Zr = Zs + 2Zp.
To keep balanced loading, designers often use 3 or 4 planets equally spaced.
Real torque gain is lower than ideal because of mesh losses, bearing losses, lubrication drag, and manufacturing tolerances.
For heavy-duty use, check bending stress, pitting resistance, carrier stiffness, and bearing life.

Example

If you choose Zs = 30, Zr = 70, hold the ring fixed, and drive the sun at 1000 RPM, the carrier output is 300 RPM. The ratio is 3.333:1 reduction with the same direction of rotation.

FAQ

Is this calculator for compound planetary sets?

No. This version is for a simple planetary set (single sun, single ring, one carrier group).

Does the ratio include efficiency?

No. Ratio is kinematic. Use your measured or estimated drivetrain efficiency separately for power/torque estimates.

Can I use negative RPM?

Yes. Negative input speed simply represents opposite rotation direction and is handled by the equations.