Planetary Gear Train Calculator

CE Style

Inputs

For internal gear sets, Zr should be > Zs.

Key Results

Member Speeds

Fundamental relation: (ωs − ωc)/(ωr − ωc) = − Zr/Zs

How to use this calculator

Boost Guide

Quick start

  1. Select Fixed member: Ring, Sun, or Carrier.
  2. Choose the Input member (the other free member).
  3. Enter Sun teeth Zs and Ring teeth Zr.
  4. Set Input speed and direction, then click Calculate.
Fundamental relation: (ωs − ωc)/(ωr − ωc) = − Zr/Zs.

Modes

  • Ring fixed (ωr=0): Sun ↔ Carrier coupling. Same direction. ωc = ωs / (1 + Zr/Zs)
  • Sun fixed (ωs=0): Ring ↔ Carrier coupling. Same direction. ωc = (Zr/Zs) · ωr / (1 + Zr/Zs)
  • Carrier fixed (ωc=0): Internal mesh. Opposite directions. ωr = − ωs · Zs/Zr

Inputs

  • Zs, Zr: For internal gears choose Zr > Zs.
  • Fixed member: The member held at zero speed.
  • Input member & speed: Pick Sun/Ring/Carrier (as allowed) and specify RPM & direction.

Results

  • Overall ratio R (in/out): magnitude |nin| / |nout|.
  • Speed reduction k (out/in): |nout| / |nin|.
  • Output speed & direction, plus ωs, ωc, ωr.

Examples

  • Ring fixed: Zs=20, Zr=60 (g=3), input Sun 1200 RPM CW → Carrier ≈ 1200/(1+3)=300 RPM CW.
  • Sun fixed: same gears, input Ring 600 RPM CW → Carrier ≈ (3/4)·600=450 RPM CW.
  • Carrier fixed: same gears, input Sun 1200 RPM CW → Ring ≈ −1200/3=−400 RPM (CCW).

Notes & limits

  • Speeds only (ideal kinematics). Torque/efficiency not computed.
  • Planet tooth count doesn’t change speeds; typical Zp=(Zr−Zs)/2 for equal planets (not enforced).
  • If Zr ≤ Zs, the set may be non-physical for internal gearing.
  • As output speed → 0, ratio → ∞ (approaches a locked condition).
FAQ & Troubleshooting

No results or “–” values

  • Enter valid numbers for Zs, Zr, and input RPM.
  • Ensure the chosen Input member is allowed for the selected fixed member.

Direction looks wrong

  • Carrier fixed → Sun & Ring rotate in opposite directions by definition.
  • Ring or Sun fixed → Input & output rotate in the same direction.

What does the ratio mean?

  • R (in/out): how many input turns per output turn (magnitude).
  • k (out/in): speed reduction factor (≤1 for reductions).

Can I model compound/idle trains?

  • This tool is single-stage. For multi-stage or Ravigneaux/compound sets, cascade stage ratios externally.

Copy-Paste Mini Workflow

1) Choose fixed member: Ring / Sun / Carrier
2) Choose input member (one of the free members)
3) Enter teeth: Zs (sun), Zr (ring)
4) Enter input speed and direction
5) Press Calculate
6) Read ratio R (in/out), reduction k (out/in), output speed & direction, and member speeds ωs, ωc, ωr