Motor & Gear Ratio Calculator
Size a motor and gear train for a target speed and torque, or for a mass or inertia you need to accelerate. FRC mode adds motor presets and a gear catalog.
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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How it works
Total ratio is driven teeth over driver teeth, multiplied across every stage. A 3:1 reduction divides speed by 3 and, before losses, multiplies torque by 3. What trips people up is the motor: it slows as the load rises, so output speed under load is lower than free speed divided by the ratio.
How to use the calculator
- 1Start with the target: a fixed output speed and torque, a mass to accelerate in a line, or an inertia to spin up. The acceleration modes turn the last two into speed and torque for you.
- 2Enter the motor’s free speed, free current, stall torque, and stall current from its datasheet, and how many motors share the load.
- 3Add the gear stages from the motor to the output. Leave mesh efficiency at 97% unless you know your gears lose more.
- 4Compare your ratio with the recommended one. If the motor lands in the stall-risk region, add a motor or cut the load. More reduction only slows the output.
Two-stage reduction on the default load
- Inputs
- A 12 V motor with 6,000 rpm free speed, 2 A free current, 3 N·m stall torque, and 145 A stall current drives 12:48 then 18:66 gears at 97% per mesh. The load is 8 lbf·ft at 300 rpm.
- Result
- Total ratio 14.67:1 at 94.1% efficiency. The motor runs at 4,428 rpm and 39.5 A, and the output turns at about 302 rpm. The recommended ratio is 14.81:1.
Free speed divided by the ratio would be 409 rpm, but carrying the load pulls the motor down to 74% of free speed. It makes 0.79 N·m, 26% of stall torque, at 77% efficiency.
What to know before using the result
- How do I pick a gear ratio for a motor?
- Divide the speed the motor will turn under load by the output speed you want. Under load that is well below free speed, so the calculator solves it from the motor’s torque curve and shows the result as the recommended ratio.
- Why does the calculator show two ratios for the same target?
- A motor can make the same power at two points on its curve: fast with little current, or slow with a lot. In the example the other point needs a 5.19:1 ratio and 108 A at 28% efficiency, against 14.81:1 and 39 A at 77%. The calculator recommends the fast point.
- Does more reduction mean more power?
- No. Reduction trades speed for torque and the power stays the same, less losses. The load needs torque times speed divided by efficiency: 341 W at the output in the example and 362 W at the motor shaft. Only more motors or a lighter load change that.
- Where do I find the motor numbers?
- Vendor datasheets list free speed, free current, stall torque, and stall current at a stated voltage. Enter the values for the voltage you run, because the calculator does not rescale them. FRC mode loads them for common motors.
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.
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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