Power transmission calculator

Linear Acceleration & Motor Calculator

Calculate drive force, wheel or drum torque, output RPM, power, time to speed, and a practical motor reduction from a motion target.

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

Diameter where shaft rotation becomes linear travel or cable motion.
Rolling resistance, drag, grade, or process force.
Drive force
15.5 lbf
Time to speed
1 s
Distance
5 ft

Derived output target: 572.96 rpm · 2.59 lbf·ft · 211 W peak at target speed

Entered ratio
14.6667:1
Predicted speed
374.39 rpm
Speed vs. target
-34.7%
Efficient ratio
9.029:1
Motor at target
5,173.28 rpm · 21.7 A
Required power / motor
224 W · 47.5% peak
Desired output is inside the recommended continuous band
Each motor runs at 86.2% of free speed, 13.8% of stall torque, 86% modeled efficiency, and 21.7 A.

Drivetrain and Custom motor performance

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

5,173.28 rpm · 21.7 A

Motor input

5,491.06 rpm

0.19 lbf·ft

12T → 48T
4:1

Shaft 1

1,372.76 rpm

0.73 lbf·ft

18T → 66T
3.667:1

Mechanism output

374.39 rpm

2.59 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 211 W at the output. With 94.1% drivetrain efficiency, each motor must deliver 224 W at its shaft. The calculator selects the higher-efficiency of the two motor-curve points that produce this power.

Efficient solution
Motor speed
5,173.28 rpm · 86.2%
Current per motor
21.7 A
Motor efficiency
86% · 99.1% of max
Required shaft power
224 W · 47.5% peak
Ratio for desired speed
9.029:1

Estimated electrical input at this point is 260 W per motor · 260 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 linear acceleration calculator works

Linear acceleration requires drive force equal to mass times acceleration plus resistance. Wheel or drum radius converts that force to output torque, while target linear speed sets output RPM and mechanical power.

How to use the calculator

  1. 1Enter the moving mass, target acceleration, target speed, and any rolling, drag, grade, or process resistance.
  2. 2Enter the wheel, pulley, or drum diameter that converts shaft rotation into linear motion.
  3. 3Enter the motor data, motor count, gear stages, and estimated mesh efficiency.
  4. 4Compare drive force, time and distance to speed, output torque, power, and the recommended motor ratio.

Worked example

50-pound mechanism acceleration

Inputs
A 50 lb moving mass accelerates at 10 ft/s² to 10 ft/s through a 4 in wheel with no added resistance.
Result
Drive force ≈ 15.5 lbf, output speed ≈ 573 rpm, and peak power ≈ 211 W.

The target speed is reached in one second and five feet. Wheel radius converts the calculated force into the required output torque.

Common questions

What to know before using the result

What does wheel or drum diameter mean?
It is the effective diameter where the mechanism produces linear motion, such as the loaded wheel diameter or the cable pitch diameter on a winch drum.
How do I include rolling resistance or drag?
Enter the opposing force as additional resistance. The calculator adds it to mass-times-acceleration force before calculating output torque and power.
Does this include traction or wheel slip?
No. Check available friction, weight transfer, drivetrain compliance, and surface conditions separately to confirm the calculated force can reach the ground.

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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