Power transmission calculator

FRC Gear Ratio & Motor Calculator

Size an FRC drivetrain or mechanism with motor presets, then match the ratio to stocked gears from AndyMark, REV, SDS, and WCP.

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

FRC COTS gear catalog

48 results

Find gears matching the tooth counts in your stages, or browse all 476 listings from AndyMark, REV Robotics, Swerve Drive Specialties, and WestCoast Products.

ReCalc source
ManufacturerPart / SKUTeethPitchBoreProduct
AndyMarkam-074112T 20 DP 8mmView part
AndyMarkam-0741AUS12T 20 DP 8mmView part
AndyMarkam-421218T 20 DP 1/2" HexView part
AndyMarkam-353418T 20 DP 3/8" HexView part
AndyMarkam-488018T 20 DP 8mmView part
AndyMarkam-439548T 20 DP 1/2" HexView part
AndyMarkam-471448T 20 DP 1/2" HexView part
AndyMarkam-514248T 20 DP 3/8" HexView part
REV RoboticsREV-21-200012T 20 DP 8mmView part
REV RoboticsREV-21-192018T 20 DP 1/2" HexView part
REV RoboticsREV-21-193548T 20 DP 1/2" HexView part
REV RoboticsREV-21-301848T 20 DP MAXSplineView part
REV RoboticsREV-21-194466T 20 DP 1/2" HexView part
REV RoboticsREV-21-302766T 20 DP MAXSplineView part
WestCoast ProductsDIS-004212T 20 DP 8mmView part
WestCoast ProductsDIS-004312T 20 DP 8mmView part
WestCoast ProductsWCP-090112T 20 DP 8mmView part
WestCoast ProductsWCP-113612T 20 DP 8mmView part
WestCoast ProductsWCP-049312T 20 DP FalconView part
WestCoast ProductsWCP-101012T 20 DP SplineXSView part
WestCoast ProductsWCP-101112T 20 DP SplineXSView part
WestCoast ProductsWCP-134912T 20 DP SplineXSView part
WestCoast ProductsWCP-135012T 20 DP SplineXSView part
WestCoast ProductsWCP-070018T 20 DP 1/2" HexView part
WestCoast ProductsWCP-073318T 20 DP 1/2" HexView part
WestCoast ProductsWCP-209218T 20 DP 1/4" RoundView part
WestCoast ProductsWCP-209318T 20 DP 1/4" RoundView part
WestCoast ProductsWCP-043218T 20 DP 3/8" HexView part
WestCoast ProductsWCP-068218T 20 DP 3/8" HexView part
WestCoast ProductsWCP-165018T 20 DP 8mmView part
WestCoast ProductsWCP-138418T 20 DP SplineXSView part
WestCoast ProductsWCP-164118T 20 DP SplineXSView part
WestCoast ProductsWCP-013748T 20 DP 1/2" HexView part
WestCoast ProductsWCP-018148T 20 DP 1/2" HexView part
WestCoast ProductsWCP-018848T 20 DP 1/2" HexView part
WestCoast ProductsWCP-011448T 20 DP 3/8" HexView part
WestCoast ProductsWCP-108948T 20 DP SplineXLView part
WestCoast ProductsWCP-119848T 20 DP SplineXLView part
WestCoast ProductsWCP-014266T 20 DP 1/2" HexView part
WestCoast ProductsWCP-017166T 20 DP 1/2" HexView part
WestCoast ProductsWCP-143066T 20 DP 1/2" HexView part
WestCoast ProductsWCP-109866T 20 DP SplineXLView part
WestCoast ProductsWCP-120766T 20 DP SplineXLView part
AndyMarkam-414612T 20 DP Falcon SplineView part
AndyMarkam-562812T 20 DP Kraken SplineView part
AndyMarkam-563318T 20 DP Kraken SplineView part
REV RoboticsREV-21-401212T 20 DP 15T SplineView part
REV RoboticsREV-21-400818T 20 DP 15T SplineView part

Ratios use actual tooth counts. Check the linked product page for pressure angle, availability, and modified center-distance spacing.

3

Motion target and results

rpm
Entered ratio
14.6667:1
Predicted speed
301.91 rpm
Speed vs. target
+0.6%
Efficient ratio
12.44:1
Motor at target
4,146.64 rpm · 46.2 A
Required power / motor
362 W · 76.9% peak
Efficient point for the required power
Selected the higher-speed, lower-current point: 69.1% of free speed, 30.9% of stall torque, 72.6% modeled efficiency, and 46.2 A per motor. The ratio aims 11% past your target speed so the robot still reaches it on a sagging battery.

Drivetrain and Custom motor performance

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

4,146.64 rpm · 46.2 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
4,146.64 rpm · 69.1%
Current per motor
46.2 A
Motor efficiency
72.6% · 83.7% of max
Required shaft power
362 W · 76.9% peak
Ratio for desired speed
12.44:1

Estimated electrical input at this point is 554 W per motor · 554 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

Pick the motor, enter what the mechanism must do, and the calculator gives the ratio that puts each motor at an efficient point. Then match it to stocked gears. Free speed is a ceiling: the battery sags and the drivetrain loses speed. In FRC mode the recommended ratio aims about 11% past your target speed, so a robot on a sagging battery still reaches it.

How to use the calculator

  1. 1Pick the motor preset and set how many share the load. Four swerve drive motors push together, so enter 4.
  2. 2For a drivetrain, use linear acceleration: robot weight, the acceleration and top speed you want, and the loaded wheel diameter. Keep the acceleration under what the carpet can grip.
  3. 3Enter the ratio you are considering, or press Match stages to target, and check the current each motor draws.
  4. 4Open the catalog on Matching stages to find stocked gears with those tooth counts. Pick one DP, then check center distance.

Worked example

125 lb robot, four Kraken X60s

Inputs
Linear mode, Kraken X60 (FOC) preset, 4 motors, 125 lb, 10 ft/s² up to 15 ft/s, 4 in wheels, two meshes at 97%.
Result
Drive force 38.9 lbf, wheels at 859 rpm, 790 W at the wheels. The recommended ratio is 5.81:1, with each motor at 22.6 A and 96% of free speed.

Speed is reached in 1.5 s over 11.25 ft. The ratio is solved for 955 rpm, 11% past the 859 rpm target, which is why it is lower than the 6.49:1 that hits 859 rpm exactly. On a battery sagging to 11 V the wheels turn about 872 rpm, so the robot still gets to speed. See the questions below.

Common questions

What to know before using the result

Does a 40 A breaker limit a motor to 40 A?
No. FRC breakers are thermal and pass more than their rating for a short time, under about a second per WCP. Rule R621 only requires a breaker of 40 A or less on each motor circuit. Turn on the calculator’s current cap only if you will set the same limit on the controller.
How much torque does a motor make at 40 A?
The table below lists it. A Kraken X60 in FOC mode makes about 0.74 N·m at 40 A, which gives 414 W in this model against 409 W in WCP’s test data.
Why is my robot slower than the calculated speed?
Free speed is with no load and a full battery. Chief Delphi posters tracked real drivetrains at about 90% of design speed, and over 95% with fewer stages. A loaded robot battery sags to about 11 V, which cuts free speed, stall torque, and stall current by 11/12. So in FRC mode the recommended ratio aims about 11% past your target speed. In the example above, a ratio solved for exactly 859 rpm gives only 785 rpm at 11 V, 91% of the target. The 5.81:1 ratio gives 872 rpm. The extra margin also covers friction the model leaves out. Use General mode for the exact ratio.
Should I set a stator or a supply current limit?
The stator limit caps motor current, which is torque. CTRE says to set it below the current where the wheels slip, and gives 120 A for a swerve drive. The supply limit caps battery draw to avoid brownouts, and CTRE gives 70 A for a swerve drive. Find both by testing.
Does the catalog match gears by tooth count alone?
Yes, by tooth count and DP. Some small pinions are addendum-modified and space like a bigger gear. ReCalc notes that the WCP-1720 has 16 teeth but spaces like 18, so check the center distance before you draw the plate.

Reference

FRC motor presets

The endpoints the calculator loads at 12 V. Torque at 40 A comes from the straight-line model. The Falcon 500 and Kraken X44 are trapezoidal and the Kraken X60 is FOC.

MotorFree speed (rpm)Free current (A)Stall torque (N·m)Stall current (A)Torque at 40 A (N·m)
Kraken X60 (FOC)5,80029.374830.74
Kraken X447,75834.112790.55
Falcon 5006,3801.54.692570.71
NEO V1.15,6761.82.61050.96
NEO Vortex6,7843.63.62110.63
NEO 55011,0001.40.971000.38

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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