Power transmission calculator
Compound Gear Ratio Calculator
Calculate the total reduction, output RPM, torque, efficiency, and shaft-by-shaft power flow for a multi-stage compound gear train.
Input → stages → output
Edit any value and the drivetrain, target, and motor curves update immediately.
Motor input
Gear stages
14.6667:1 totalMotion target and results
- 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
Drivetrain and Custom motor performance
RPM and torque through each shaft, followed by the interpreted motor curves.
Motor input
4,428.02 rpm
0.58 lbf·ft
Shaft 1
1,107.01 rpm
2.25 lbf·ft
Mechanism output
301.91 rpm
8 lbf·ft
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.
- 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 this compound gear ratio calculator works
A compound gear train multiplies the driven-to-driver tooth ratio of every stage. The combined reduction divides motor speed, multiplies ideal torque, and compounds the entered mesh loss at each stage.
How to use the calculator
- 1Enter the motor speed, torque, voltage, and torque-speed endpoints, or keep the generic motor values for a ratio-only estimate.
- 2Add each gear stage in order from the motor to the mechanism and enter its driver and driven tooth counts.
- 3Set the per-stage mesh efficiency, then compare the total ratio, output speed, torque, and shaft flow.
- 4Edit the stages or match them to a desired output target while preserving practical tooth sizes, center distances, and load capacity.
Worked example
Two-stage 12:1 reduction
- Inputs
- A 12-tooth gear drives 48 teeth, followed by an 18-tooth gear driving 54 teeth, at 6,000 motor rpm.
- Result
- Total ratio = 12:1 and ideal output speed = 500 rpm.
The 4:1 first stage and 3:1 second stage multiply to 12:1. Output torque is multiplied by the same ideal ratio before mesh losses.
Common questions
What to know before using the result
- How are compound gear ratios calculated?
- Divide driven teeth by driver teeth for each stage, then multiply all stage ratios. Gears fixed to the same intermediate shaft rotate at the same speed and create the compound stages.
- Does an idler gear change the ratio?
- A simple idler changes rotation direction or spacing but not the ratio magnitude. It contributes another mesh loss unless it is part of a compound shaft arrangement.
- How does stage efficiency affect output torque?
- Ideal torque multiplication is reduced by the product of all stage efficiencies. A train with more meshes usually loses more power even when its overall ratio is unchanged.
Formula
F = ma + Fᵣ · T = Fr · P = Fv · GR = ∏(N driven ÷ N driver)
Linear mode uses F = ma and drive radius; angular mode uses τ = Iα plus resisting torque. Multiply each gear-stage ratio for total reduction; required motor-shaft power also includes drivetrain losses.
Engineering references
Assumptions and limits
- Each listed row represents one external gear mesh between a driver and a driven gear.
- Gears on the same compound shaft rotate at the same speed and do not add another mesh.
- Torque excludes bearing, windage, lubrication, and other losses beyond the entered mesh efficiency.
- Required power is the steady-state power at the entered speed and torque; acceleration requires additional power and energy.
- Linear acceleration mode assumes constant acceleration from rest, constant drive radius, no wheel slip, and the entered resistance force. Its displayed power is the instantaneous mechanical output required at target speed.
- Angular acceleration mode assumes constant acceleration from rest, fixed rotational inertia, and the entered resisting torque.
- Motor curves are ideal constant-voltage approximations from entered or published free-speed, free-current, stall-torque, and stall-current endpoints.
- No current cap is applied by default. The optional cap represents a configured motor-controller setting, not a branch-breaker rating.
- Breaker trips are time- and temperature-dependent; battery sag, controller mode, current limiting, temperature, and manufacturing variation change real motor performance.
- Pitch, pressure angle, tooth form, center distance, and interference must be checked separately.
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