How much acceleration can the wheels actually deliver?

No more than the friction coefficient times g, times the share of weight on the driven wheels. With a coefficient near 1 that is about 1 g, or 32 ft/s². To measure the coefficient, tilt a ramp covered in your floor material until a weighted frame slides. The tangent of that angle is the coefficient.

Once the wheels slip, does more gear reduction help?

Not for pushing force. A traction-limited drive pushes with weight times coefficient, whatever the ratio. More reduction can still cut battery draw and heat.

Do spinning parts count as mass?

Yes. A wheel adds its inertia divided by its radius squared, which is half its own mass for a solid disc. A motor rotor adds its inertia times the ratio squared, which grows fast at high reduction. The calculator includes neither, so add a rough allowance to the mass.

What wheel diameter do I enter?

The rolling diameter under load. A rubber tread compresses, so it is a bit under the nominal size. On a winch drum use the cable pitch diameter, which is the drum plus one cable width and grows with each layer of cable.

Power transmission calculator

Linear Acceleration & Motor Calculator

Turn a mass, an acceleration, and a top speed into drive force, wheel torque, wheel rpm, and power, then check them against a motor.

Input → stages → output

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

Calculator mode

Motor input

Use any motor’s published endpoint data

Motors

Voltage

Free speed

rpm

Stall torque

Free current

Stall current

Controller current cap

Not applied

Gear stages

14.6667:1 total

Efficiency / mesh

Stage 1

Driver

Driven

Stage 2

Driver

Driven

Motion target and results

Moving mass

Acceleration

Target speed

Driven wheel or drum diameter

Diameter where shaft rotation becomes linear travel or cable motion.

Additional resistance

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

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 it works

Drive force is mass times acceleration plus any resistance. Multiply by the wheel radius for torque, and divide the target speed by the wheel circumference for rpm. Check the force against what the wheels can grip, which is the friction coefficient times the weight on them, before sizing a motor for it.

How to use the calculator

1Enter the mass and the acceleration you want. If you only know a time to speed, acceleration is speed divided by time.
2Add resistance as a force: rolling drag, or weight times sin(angle) on a slope. Measure rolling drag with a force gauge if you can.
3Enter the diameter where force reaches the ground or rope. That is the loaded wheel diameter, or the cable pitch diameter on a winch drum.
4Compare the drive force with the traction limit. If the target is higher, no motor will reach it, so lower the acceleration.

Key formulas

Linear acceleration formulas

Drive force: F = m × a + F resist; On a slope, add m × g × sin(angle) to the resistance.
Wheel torque and speed: T = F × D ÷ 2 · n = 60 × v ÷ (π × D); D is the loaded wheel or drum diameter, v the target speed in m/s.
Peak output power: P = F × v; Reached at the end of the run, when speed is highest.
Time and distance to speed: t = v ÷ a · d = v² ÷ (2 × a)

Worked example

50 lb mechanism to 10 ft/s in one second

Inputs: A 50 lb mass accelerates at 10 ft/s² to 10 ft/s through a 4 in wheel, with no added resistance. The motor is the default one (6,000 rpm free speed, 3 N·m stall torque) through two 97% meshes.
Result: Drive force 15.5 lbf, wheel torque 2.59 lbf·ft, 573 rpm, and 211 W at the wheel, reached in 1.0 s over 5 ft. The recommended ratio is 9.03:1, at 21.7 A.

F = 22.68 kg × 3.048 m/s² = 69.1 N. Torque = 69.1 N × 0.0508 m = 3.51 N·m. Speed = 3.048 m/s ÷ (π × 0.1016 m) × 60 = 573 rpm. Power = 69.1 N × 3.048 m/s = 211 W, and the motor shaft supplies 224 W after the 94.1% mesh efficiency.

Common questions

What to know before using the result

How much acceleration can the wheels actually deliver?: No more than the friction coefficient times g, times the share of weight on the driven wheels. With a coefficient near 1 that is about 1 g, or 32 ft/s². To measure the coefficient, tilt a ramp covered in your floor material until a weighted frame slides. The tangent of that angle is the coefficient.
Once the wheels slip, does more gear reduction help?: Not for pushing force. A traction-limited drive pushes with weight times coefficient, whatever the ratio. More reduction can still cut battery draw and heat.
Do spinning parts count as mass?: Yes. A wheel adds its inertia divided by its radius squared, which is half its own mass for a solid disc. A motor rotor adds its inertia times the ratio squared, which grows fast at high reduction. The calculator includes neither, so add a rough allowance to the mass.
What wheel diameter do I enter?: The rolling diameter under load. A rubber tread compresses, so it is a bit under the nominal size. On a winch drum use the cable pitch diameter, which is the drum plus one cable width and grows with each layer of cable.

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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