How is output torque calculated from gear ratio?

Output torque T_out = T_in x GR x efficiency. For a speed reduction (GR > 1), torque is multiplied. For a speed increase (GR < 1), torque is divided. Efficiency accounts for friction losses in bearings, tooth mesh, and seals, typically 95 to 99% per stage for spur gears.

What is the gear ratio of a planetary gearset?

For a standard planetary gearset with sun gear S, ring gear R, and planet carrier C (fixed ring, input sun, output carrier): GR = 1 + R/S. With a fixed sun and input ring: GR = 1 + S/R. With a fixed carrier: GR = -R/S (ring and sun rotate in opposite directions). This calculator uses the fixed-ring (most common) configuration.

What is typical gear efficiency for spur and helical gears?

Per mesh efficiency: spur gears 98 to 99.5%, helical gears 98 to 99%, worm gears 50 to 90% depending on lead angle, bevel gears 97 to 99%. Belt drives (V-belt) 94 to 97%, synchronous belt 97 to 99%, roller chain 97 to 99%. These values are per stage; overall efficiency is the product of all stage efficiencies.

What is the difference between a compound and simple gear train?

A simple gear train has one gear on each shaft. A compound gear train has two gears on intermediate shafts (one driven, one driving the next stage), allowing much higher overall ratios in a compact package. The overall ratio of a compound train is the product of each stage ratio, while for a simple train it is just the ratio of first to last gear.

Gear Ratio, Speed & Torque Calculator – Multi-Stage, Planetary & Belt | CalcEngines

Mechanical Engineering Tools · CalcEngines

Gear Ratio, Speed & Torque Calculator

Advanced multi-stage gear train calculator. Build up to 4 stages with spur/helical gears, planetary gearsets, belt drives, or chain drives — with live efficiency and power loss tracking.

Up to 4 stages Spur & helical Planetary Belt & chain Efficiency cascade SI & Imperial

Input Shaft Conditions

Input Speed n_in

RPM

Driver / motor speed

Input Torque T_in

Input shaft torque

Input Power P_in

Auto-calculated from T×ω

Quick Presets

Gear Stages

Imperial

Drivetrain Flow

Add at least one stage and calculate.

Output Results

Power & Efficiency Summary

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Stage-by-Stage Breakdown

Stage	Type	Ratio GR	Shaft Speed	Shaft Torque	Efficiency	Power Loss
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All Values & Unit Conversions

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Formula Reference

Drive Type	Gear Ratio	Output Speed	Output Torque
Spur / helical gear pair	GR = N_driven / N_driver	n_out = n_in / GR	T_out = T_in × GR × η
Planetary (fixed ring)	GR = 1 + N_ring / N_sun	n_carrier = n_sun / GR	T_out = T_in × GR × η
Belt drive	GR = D_driven / D_driver	n_out = n_in / GR	T_out = T_in × GR × η
Chain drive	GR = N_{driven sprocket} / N_driver	n_out = n_in / GR	T_out = T_in × GR × η
Compound (multi-stage)	GR_total = GR₁ × GR₂ × …	n_out = n_in / GR_total	η_total = η₁ × η₂ × …
Input power	P = T × 2πn / 60	P in watts, T in N·m, n in RPM	P_out = P_in × η_total

Typical efficiency per stage: Spur gears 98–99.5% · Helical gears 98–99% · Planetary 97–99% · V-belt 94–97% · Synchronous belt 97–99% · Roller chain 97–99%

Common Questions

How is gear ratio calculated from tooth counts? +

For a simple gear pair: GR = N_driven / N_driver. If GR > 1, the driven gear rotates slower (speed reduction, torque multiplication). For a compound train, the overall ratio is the product of all stage ratios: GR_total = GR₁ × GR₂ × ...

Why does torque increase when speed is reduced? +

Conservation of energy: ignoring losses, power is constant through the drivetrain (P = T × ω). If speed drops by factor GR, torque must rise by the same factor to maintain power: T_out = T_in × GR × η. This is why gearboxes allow small motors to move heavy loads slowly.

What is a planetary gearset? +

A planetary (epicyclic) gearset has a central sun gear, multiple planet gears orbiting it, an outer ring gear, and a planet carrier. With the ring gear fixed, input on the sun, and output on the carrier: GR = 1 + N_ring/N_sun. Planetary sets achieve high ratios in compact space and are used in automatic transmissions, hub gears, and gearboxes.

How does drivetrain efficiency compound across stages? +

Overall efficiency is the product of all stage efficiencies: η_total = η₁ × η₂ × ... A 4-stage system with 98% efficiency per stage gives η_total = 0.98⁴ ≈ 92.2%. This is why minimising the number of stages (or using high-efficiency types) matters in high-power drivetrains.

What is the difference between a speed ratio and torque ratio? +

The speed ratio and ideal torque ratio are reciprocals of each other. If GR = 4 (speed is quartered), ideal torque is multiplied by 4. In practice, friction losses mean T_out = T_in × GR × η, so actual torque multiplication is slightly less than GR. Power out is always less than power in by the factor η_total.