Stepper Motor Torque Requirement Estimator

A 0.4 N·m NEMA 17 is plenty for a light print head and not enough for a 10 kg steel gantry at 10 m/s². This estimator uses F = ma plus friction on a horizontal axis, or F = m(a + g) when the axis lifts the load, then turns the force into torque through a belt pulley or a screw.

Inputs

Units

Results

Linear force: 6.98N
Required torque: 4.94N·cm
With 1.5× safety: 7.41N·cm

The Result is indicative and educational. It does not constitute a design, a technical opinion or medical advice and does not replace calculations or verification by a person with the appropriate qualifications and authorisations. Before purchase, installation or use in practice – in particular in electrical installations – the Result should be verified by a qualified specialist. Details: Terms of Service, point 4.

Example products

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Calculation method

On a horizontal axis the linear force is F = m a + μ m g: mass times acceleration, plus guide friction from the weight pressing on the rails. On a vertical axis that lifts the load, F = m (a + g): the motor carries the whole weight and accelerates it upward, and μ is not applied because the weight does not press on the guides. Acceleration converts from mm/s² to m/s² (÷ 1000) and g = 9.80665 m/s². For a GT2 belt, pitch diameter = (teeth × 0.002 m) / π, radius is half of that and torque = F r / efficiency. For a lead screw, torque = F × lead / (2 π × efficiency) with lead in metres. Outputs are N·cm (×100 from N·m); imperial shows oz·in. Recommended torque is 1.5× the calculated value. Belt mode ignores lead; screw mode ignores pulley teeth.

Exact formula

Horizontal: F = m a + μ m g. Vertical (lifting): F = m (a + g). Belt: T = F r / η with r from the GT2 pitch diameter. Screw: T = F × lead / (2 π η). Recommended = 1.5 × T. Efficiency is a decimal (0.9 belt; 0.3–0.75 trapezoidal screw). Limits: Ignores motor rotor inertia, belt stretch and the loss of stepper torque with speed. GT2 pitch diameter assumes 2 mm pitch. The 1.5× factor is a shop safety, not a datasheet.

Acceleration units

Firmware often uses mm/s². 3000 mm/s² is a mild printer accel; 10 000 is sporty. A heavy CoreXY gantry may sit lower until input shaper is tuned.

Dual motors

Two Z screws share the load: enter the mass each motor lifts, about half the gantry for two screws or a third for three. Use the full mass only when one motor lifts everything, for example two screws linked by a belt to a single motor.

Frequently asked questions

N·cm vs N·m vs oz·in?

1 N·m = 100 N·cm ≈ 141.6 oz·in. Desktop motors are often 40–60 N·cm holding.

Why is screw torque lower for the same mass?

A fine lead is a large reduction. You pay with speed and often with efficiency (more friction).

What about a Z axis?

Choose Vertical: the force becomes m × (a + g), so the weight dominates — 1 kg needs about 9.8 N before any acceleration. Enter the mass each motor lifts. A 2 mm lead screw self-locks when the motor is off; TR8×8 screws and belted Z axes can drift down under their own weight.

Does this include a toolhead full of filament?

Put the moving mass you actually accelerate — toolhead, rails, and a partial spool if it rides along. Do not add the whole printer frame.

What μ should I use?

0.02–0.05 for decent linear rails, 0.1+ if wheels are overtight or the axis is dirty. If the axis is hard to push by hand, μ is not 0.02. A vertical axis ignores μ.