3D Printing Calculators

FDM hardware & mechanics

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, then torque through a belt pulley or screw.

Inputs

Units
kg

Gantry + tool. Imperial shows pounds.

mm/s²

3000 mm/s² is 3 m/s². Printers often use 3000–10000; heavy CoreXY gantries less.

Low for wheels/rails (0.02–0.08). Higher if the axis binds.

Used when drive is belt. Pitch 2 mm.

mm

Used when drive is lead screw. TR8×8 is 8 mm/rev.

Belt ~0.85–0.95. Trapezoidal screw ~0.3–0.5. Ball screw higher.

Results

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

Compare to the motor’s holding torque. Running torque is lower.

Recommended gear

Calculation method

Linear force F = m a + m g μ with a in m/s² (mm/s² ÷ 1000) and g = 9.80665 m/s². For a GT2 belt, pitch diameter = (teeth × 0.002 m) / π, radius is half of that, 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

F = m a + m g μ. Belt: T = F r / η with r from GT2 pitch diameter. Screw: T = F × lead / (2 π η). Recommended = 1.5 × T. Efficiency is a decimal (0.9 belt, 0.4 screw typical). Limits: Ignores motor inertia and belt stretch. 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 load if they share the mass. Do not double the torque requirement unless each motor drives the full mass (poorly coupled dual drive).

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).

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.

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