How many planet gears should a planetary gearbox have?

Most planetary gearboxes use 3 to 5 planet gears. Three planets are most common as they are easiest to assemble and provide balanced loading. Four or five planets increase torque capacity and reduce tooth loads, but require more precise manufacturing. The tooth counts must satisfy the assembly condition: (N_sun + N_ring) must be divisible by the number of planets.

What is the difference between a planetary and epicyclic gear train?

The terms are interchangeable. An epicyclic gear train is the academic/mathematical name; planetary gearbox is the common engineering name. Both describe a system of a central sun gear, outer ring (annulus) gear, and planet gears mounted on a rotating carrier.

What is the maximum gear ratio for a single-stage planetary gearbox?

A single-stage planetary gearbox typically achieves ratios between 3:1 and 10:1. The theoretical maximum with ring fixed is limited by the ring-to-sun tooth ratio, practically around 12:1 before tooth geometry becomes impractical. For higher ratios, compound or multi-stage planetary systems are used, achieving up to 100:1 or more.

Planetary Gear Train Calculator – Gear Ratio, Speed & Torque | CalcEngines

Mechanical Power Transmission · CalcEngines

Planetary Gear Train Calculator

Advanced epicyclic gear calculator — ratio, output speed, torque, efficiency, gear geometry, and assembly validation for all Sun/Ring/Carrier configurations.

All 3 Configurations Gear Geometry Assembly Check Torque & Efficiency Free to use

Configuration — Select Fixed Element & I/O

Tooth Counts

Sun Gear Teeth (N_s) Typically 12 – 40 teeth

Ring Gear Teeth (N_r) Must be > N_s + 2×N_p

Number of Planets Assembly condition checked

Operating Parameters

Input Speed (RPM) Motor / prime mover speed

Input Torque (N·m) Applied input torque

Module (m) Gear module for geometry

Mesh Efficiency (%) Per planet mesh pair

Primary Results

Select a configuration, enter tooth counts, and click Calculate.

Speed & Torque Analysis

⚠ Torque note: Output torque shown is theoretical (efficiency-adjusted). Actual torque depends on bearing losses, lubrication, and thermal conditions. Always apply an appropriate service factor (SF ≥ 1.25 for industrial use).

Gear Geometry (pitch diameters, module m)

Pitch diameter formula: d = m × N · Sun: d_s = m×N_s · Planet: d_p = m×N_p · Ring: d_r = m×N_r · Carrier PCD: d_c = m×(N_s+N_p)

Assembly Condition Checks

Meshing condition: N_r = N_s + 2×N_p · Assembly condition: (N_s + N_r) ÷ N_planets = integer · Neighbour condition: Planet tip circles must not overlap

Common Planetary Stage Reference (Ring Fixed · Sun In · Carrier Out)

N_sun	N_ring	N_planet	Ratio	Output / Input	Assembly (÷3)	Assembly (÷4)	Assembly (÷5)	Carrier PCD ratio	Notes

Common Questions

What is the gear ratio formula for a planetary gear train? +

The fundamental epicyclic equation is: N_s × ω_s + N_r × ω_r = (N_s + N_r) × ω_c. With the ring fixed (ω_r=0) and sun as input: ratio = 1 + N_r/N_s. This is the most common configuration used in automotive automatic transmissions and industrial speed reducers.

How many planet gears should I use? +

3 planets is the most common choice — balanced, simple to assemble, statically determinate load sharing. 4 or 5 planets increase torque density but require tighter tolerances for load sharing. The assembly condition must be satisfied: (N_sun + N_ring) must be exactly divisible by the number of planets.

What is the difference between planetary and epicyclic gears? +

The terms are completely interchangeable. Epicyclic is the classical mathematical/kinematics term. Planetary is the common engineering and commercial name — the planets orbit the sun gear just like planets orbit a star. Both describe the same sun–planet–ring–carrier arrangement.

What gear ratio range can a single planetary stage achieve? +

A single stage with the ring fixed typically gives 3:1 to 12:1 reduction (sun in, carrier out). For the reverse (carrier in, sun out) you get the inverse — about 1:3 to 1:12 speed increase. Carrier-fixed configurations give a negative ratio (output reverses direction). For ratios beyond 12:1, compound or multi-stage planetary systems are used.

Why is planetary gearbox efficiency so high? +

Load is distributed across multiple planet gears simultaneously, reducing tooth contact forces. Coaxial I/O eliminates bending moments. Typical single-stage efficiency is 97–99%. Compare this to worm gearboxes (50–90%) or multi-stage parallel gearboxes where losses compound. The result is less heat, smaller cooling requirements, and longer life.