How do I split a big ratio into stages?

Use stages of 3:1 to 7:1 and multiply. A 100:1 reduction is about 4.6 × 4.6 × 4.6, so three stages. Match stages to target picks tooth counts from 12 to 84 and aims for stages of 7:1 or less.

Does an idler gear change the ratio?

No. The ratio depends only on the first and last gear. An idler reverses the direction of rotation and adds one more mesh loss.

How much does each extra stage cost?

At 97% per mesh, two stages keep 94.1%, three keep 91.3%, and four keep 88.5%. At the same total ratio, fewer stages lose less.

Can I change the ratio without moving the shafts?

Yes, if the tooth counts add up to the same number. Center distance is (N₁ + N₂) ÷ (2 × DP), so 24:60, 42:42, and 12:72 all fit the same spacing of 84 teeth, at 2.5:1, 1:1, and 6:1.

Power transmission calculator

Compound Gear Ratio Calculator

Multiply the stages of a compound gear train and see the speed, torque, and efficiency left at every shaft.

Input → stages → output

Edit any value and the drivetrain, target, and motor curves update immediately.

Calculator mode

Motor input

Use any motor’s published endpoint data

Motors

Voltage

Free speed

rpm

Stall torque

Free current

Stall current

Controller current cap

Not applied

Gear stages

14.6667:1 total

Efficiency / mesh

Stage 1

Driver

Driven

Stage 2

Driver

Driven

Motion target and results

Output speed

rpm

Output torque

Entered ratio: 14.6667:1
Predicted speed: 301.91 rpm
Speed vs. target: +0.6%
Efficient ratio: 14.811:1
Motor at target: 4,443.36 rpm · 39.1 A
Required power / motor: 362 W · 76.9% peak

Efficient point for the required power

Selected the higher-speed, lower-current point: 74.1% of free speed, 25.9% of stall torque, 77.2% modeled efficiency, and 39.1 A per motor.

Drivetrain and Custom motor performance

RPM and torque through each shaft, followed by the interpreted motor curves.

4,443.36 rpm · 39.1 A

Motor input

4,428.02 rpm

0.58 lbf·ft

12T → 48T

4:1

Shaft 1

1,107.01 rpm

2.25 lbf·ft

18T → 66T

3.667:1

Mechanism output

301.91 rpm

8 lbf·ft

Entered stages Efficient required-power solution Efficient continuous band 90%+ peak power · transient Low-speed stall risk Torque · 3 N·m stall Current · 145 A stall Power · 471 W modeled peak Efficiency · 87% modeled max

Most efficient solution for the required power

The movement needs 341 W at the output. With 94.1% drivetrain efficiency, each motor must deliver 362 W at its shaft. The calculator selects the higher-efficiency of the two motor-curve points that produce this power.

Efficient solution

Motor speed: 4,443.36 rpm · 74.1%
Current per motor: 39.1 A
Motor efficiency: 77.2% · 89% of max
Required shaft power: 362 W · 76.9% peak
Ratio for desired speed: 14.811:1

Estimated electrical input at this point is 469 W per motor · 469 W total at nominal voltage. This is the steady-state power for the entered speed and torque; acceleration requires additional power.

The curves are an engineering estimate, not a thermal or controller simulation. A breaker rating is not a motor-current cap; brief current can exceed that rating before a time-dependent trip. Battery or supply sag, configured controller limits, commutation, temperature, friction, and manufacturing variation change real performance.

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Quick answer

How it works

A compound train multiplies the driven-over-driver ratio of each stage. The two gears on a shared middle shaft turn at the same speed, which is how a small gear count reaches a big ratio. A gear that only sits between two others is an idler: it reverses direction and adds a mesh loss, but no ratio.

How to use the calculator

1Enter one row per mesh, in order from the motor. The driven gear of one row and the driver of the next sit on the same shaft.
2Keep each stage to 7:1 or less. A 12-tooth pinion on an 84-tooth gear is 7:1, and WCP’s 20 DP gears stop at 84 teeth.
3Read the shaft readouts. Each shows the speed and torque on that shaft. The last stage carries the most torque, so size that pair first.
4To count an idler’s mesh loss, add it as an equal-tooth row such as 24:24. It does not change the ratio.

Key formulas

Compound gear ratio formulas

Total ratio: GR = (N₂ ÷ N₁) × (N₄ ÷ N₃) × …; Driven teeth over driver teeth for each mesh. Idlers cancel out.
Output speed and torque: n out = n in ÷ GR · T out = T in × GR × ηᵏ; η is the efficiency of one mesh and k the number of meshes.
Center distance: CD = (N₁ + N₂) ÷ (2 × DP); Add the two tooth counts, so pairs with the same sum share a spacing.

Worked example

Two stages, 12:1

Inputs: A 12-tooth gear drives a 48-tooth gear. An 18-tooth gear on the same shaft as the 48 drives a 54-tooth gear. The motor and load are the calculator’s defaults (6,000 rpm free speed, 3 N·m stall torque, 8 lbf·ft at 300 rpm) at 97% per mesh.
Result: Total ratio 12:1 at 94.1%. Motor: 4,079 rpm and 0.96 N·m. Shaft 1: 1,020 rpm and 3.73 N·m. Output: 340 rpm and 10.85 N·m.

The stage ratios are 4 × 3 = 12. Each stage multiplies torque by its ratio and loses 3%: 0.96 × 4 × 0.97 = 3.73 N·m, then 3.73 × 3 × 0.97 = 10.85 N·m. The last mesh carries about 11 times the torque of the first.

Common questions

What to know before using the result

How do I split a big ratio into stages?: Use stages of 3:1 to 7:1 and multiply. A 100:1 reduction is about 4.6 × 4.6 × 4.6, so three stages. Match stages to target picks tooth counts from 12 to 84 and aims for stages of 7:1 or less.
Does an idler gear change the ratio?: No. The ratio depends only on the first and last gear. An idler reverses the direction of rotation and adds one more mesh loss.
How much does each extra stage cost?: At 97% per mesh, two stages keep 94.1%, three keep 91.3%, and four keep 88.5%. At the same total ratio, fewer stages lose less.
Can I change the ratio without moving the shafts?: Yes, if the tooth counts add up to the same number. Center distance is (N₁ + N₂) ÷ (2 × DP), so 24:60, 42:42, and 12:72 all fit the same spacing of 84 teeth, at 2.5:1, 1:1, and 6:1.

Formula

F = ma + Fᵣ · T = Fr · P = Fv · GR = ∏(N driven ÷ N driver)

Output speed is motor speed divided by total ratio. Output torque is motor torque times ratio times efficiency. Linear targets use F = ma plus resistance at the wheel radius. Angular targets use τ = Iα plus resisting torque.

Engineering references

Assumptions and limits

Each row is one external mesh between a driver and a driven gear. Gears fixed to the same shaft turn together and add no mesh. Pitch, pressure angle, and center distance are not checked.
The motor is a straight line from free speed and free current to stall torque and stall current, at constant voltage. Battery sag, heating, and controller limits move the real curve.
Efficiency is one number per mesh, applied to every row. Bearing, windage, and lubricant losses are not included.
Acceleration targets assume constant acceleration from rest and no wheel slip. The motor is checked at the target speed with full acceleration torque, the hardest point of the run.

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