Power transmission calculator

Motor & Gear Ratio Calculator

Calculate motor power and ideal ratio from linear or angular acceleration, or model output RPM and torque directly. Optional FRC mode adds motor presets and a linked COTS gear catalog.

Input → stages → output

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

Calculator mode
1

Motor input

V
rpm
A
A
2

Gear stages

14.6667:1 total
%
Stage 1
T
T
Stage 2
T
T
3

Motion target and results

rpm
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

01,5003,0004,5006,000 Motor speed (rpm) 100% 0%
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 this gear ratio calculator works

Enter output RPM and torque directly, derive them from linear acceleration through a driven wheel or drum, or derive them from rotational inertia and angular acceleration. The calculator converts the target into output torque, peak mechanical power, and an efficient motor reduction. Optional FRC mode adds motor presets and a collapsible COTS gear catalog.

How to use the calculator

  1. 1Enter any motor’s specifications, or switch to FRC mode to choose an FRC motor preset and search matching vendor gears.
  2. 2Add or edit gear stages from input to output; each stage uses driver teeth, driven teeth, and mesh efficiency.
  3. 3Choose Direct output, Linear acceleration, or Angular acceleration. Each input has its own appropriate unit selector.
  4. 4Compare the required motor power and efficient ratio, then match the editable gear stages to that target.
  5. 5Leave margin for acceleration, battery sag, thermal limits, current limiting, friction, and duty cycle.

Worked example

Single 3:1 reduction

Inputs
A 12-tooth driver turns a 36-tooth gear at 5,000 rpm with 1.0 lbf·ft input torque.
Result
Ideal output speed = 1,667 rpm and ideal output torque = 3.0 lbf·ft before losses.

A 3:1 reduction divides speed by three and multiplies ideal torque by three. Real output torque is reduced by drivetrain losses.

Common questions

What to know before using the result

Where should a DC motor normally operate?
There is no single universal point. For a required mechanical power below the motor maximum, the higher-speed, lower-torque intersection is usually more efficient; acceleration and transient loads still require torque and current margin.
How do you calculate motor power and gear ratio for acceleration?
For linear motion, required force is mass times acceleration plus resistance, and wheel or drum radius converts force and speed into shaft torque and RPM. For rotational motion, acceleration torque is rotational inertia times angular acceleration, plus resisting torque. The motor curve then determines whether the operating point is feasible and which reduction reaches it efficiently.
Does a 40 A FRC breaker limit motor current to 40 A?
No. The breaker provides time-dependent circuit protection and can carry brief current above its rating. Leave the controller current cap off unless you intend to configure an actual motor-controller limit, and evaluate breaker trip time, battery sag, wiring, heat, and duty cycle separately.
Does an idler gear change the ratio?
A simple idler changes direction and spacing but not the ratio magnitude. Compound gears fixed to the same shaft can create additional stages.
Why is required motor power higher than output power?
Mesh, bearing, belt, chain, and other losses require more shaft power upstream. The calculator applies entered stage efficiencies, but real losses vary with load and speed.
Can this calculator find FRC gears to buy?
Yes. FRC mode searches COTS gear listings from AndyMark, REV Robotics, Swerve Drive Specialties, and WestCoast Products by stage tooth count, diametral pitch, bore, manufacturer, and SKU. Each result links to the vendor product page.

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.
Educational estimate
Use this result for learning and early design exploration. Verify safety-critical or production decisions with the governing standard, material data, real tooling, and a qualified engineer.

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