planetary gear calculator

What this planetary gear calculator does

A planetary (epicyclic) gear set has three members: a sun gear, a ring gear, and a carrier that holds the planet gears. This calculator solves speed relationships for an ideal simple planetary set using tooth counts and RPM values.

It is useful for drivetrain design, robotics, e-bikes, automatic transmissions, compact reducers, and any mechanism where you need torque multiplication in a small package.

How to use it

1) Enter tooth counts

Set Ns (sun teeth) and Nr (ring teeth). In most practical designs, the ring has more teeth than the sun.

2) Enter two known speeds

Fill in any two RPM fields and leave one blank. Example: if the ring is fixed, set ring speed to 0.

3) Click calculate

The missing speed is computed and the tool also shows common fixed-member ratios:

• Sun input, ring fixed → carrier output: i = 1 + Nr/Ns
• Ring input, sun fixed → carrier output: i = 1 + Ns/Nr
• Sun to ring with carrier fixed: ωr/ωs = -Ns/Nr

Why planetary gears are so popular

• High power density: multiple planets share load.
• Coaxial layout: input and output can be on the same axis.
• Flexible kinematics: different fixed members produce reduction, overdrive, or reverse.
• Compact multi-stage options: large total ratios in smaller volume than many parallel-shaft alternatives.

Design notes and practical checks

Tooth count compatibility

For a classic simple planetary, a common geometric relation is: Np = (Nr - Ns) / 2 where Np is planet tooth count. If this is not an integer, your selected numbers may not correspond to a standard planet geometry.

Sign convention matters

RPM signs indicate direction. A negative result means the solved member rotates opposite your chosen positive direction. The math is correct as long as you stay consistent.

Ideal vs real-world performance

This calculator is kinematic only. It does not include bearing drag, mesh losses, lubrication effects, shaft compliance, backlash, thermal expansion, or load-dependent efficiency. For production design, validate with simulation and testing.

Worked example

Suppose Ns = 30, Nr = 70, sun speed is 1200 RPM, and the ring is fixed (0 RPM). Carrier speed becomes:

ωc = (Ns·ωs + Nr·ωr) / (Ns + Nr) = (30·1200 + 70·0) / 100 = 360 RPM

That means a reduction of 1200 / 360 = 3.333..., matching 1 + Nr/Ns = 1 + 70/30.

FAQ

Can I use decimal RPM values?

Yes. Speeds can be integers or decimals.

Do I need to enter planet gear teeth?

No. Speed relationships for a simple planetary depend on sun and ring tooth counts. Planet tooth count is shown only as a geometry hint.

What if I leave more than one speed blank?

Then there is not enough information for a unique solution. Provide exactly two known speeds.