Choose which part is held, which drives, and the tooth counts. Get the ratio, speeds and torques of every part, the planet bearing speed, and a check that the planets fit and can be assembled.
Held part · input → output
Zs
Zp
Number of planets
Module · ISO 54
m mm
RPM
N·m
Identical stages in series
Each stage's output drives the next stage's input, like a stacked gearhead.
Ring held · sun drives · carrier output
InputOutputHeldPlanets
Parts
Part
Teeth
Pitch Ø
Speed
Torque
Ratio finder
Enter the ratio you need for the chosen setup. Only tooth sets that fit and can be assembled with the chosen number of planets are shown.
: 1
Sun
Planet
Ring
Ratio
Error
How it is calculated
Simple planetary set with standard teeth (no profile shift): sun Zs, planets Zp, ring Zr = Zs + 2·Zp, all with the same module m. One part is held, one drives, the third is the output. Speeds follow the Willis equation.
Willis equation (n_sun − n_carrier) / (n_ring − n_carrier) = − Zr / Zs
Ring held i = 1 + Zr/Zs (sun in, carrier out)
Sun held i = 1 + Zs/Zr (ring in, carrier out)
Carrier held i = − Zr/Zs (sun in, ring out, reversed)
Planet bearing n_planet,rel = (n_sun − n_carrier) · Zs / Zp
Assembly (Zs + Zr) / N must be a whole number
Neighbour check (Zs + Zp) · sin(180°/N) > Zp + 2 (planet tips must not touch)
Pitch diameters d = m · z, center distance a = m · (Zs + Zp) / 2
Torques T_out = T_in · |i| · η, η ≈ 0.97 per stage; held part takes T_out − T_in (with sign)
Undercut appears below about 17 teeth at 20° pressure angle. Planet bearings run at the relative planet speed, not at the output speed, so size them with the value from the table.