Stepper Motor Torque Calculator
On a belt-driven axis, a stepper motor's rotary torque becomes a linear force at the belt through the pulley. The conversion is simple mechanics: force equals torque divided by the pulley pitch radius, where the pitch radius is the tooth count times the belt pitch divided by two pi. This calculator takes the motor holding torque in newton-centimeters and the pulley geometry, then returns the linear belt force in newtons and the equivalent in kilograms-force. The holding torque is a value you read from your motor's data sheet; nothing is assumed. Treat the result as a static upper bound to be derated for motion.
Torque to force formula
Pitch radius (m) = teeth * belt pitch (mm) / (2 * pi) / 1000
Torque (N-m) = holding torque (N-cm) / 100
Belt force (N) = torque (N-m) / pitch radius (m)
Belt force (kgf) = force (N) / 9.80665
The pitch circumference equals the tooth count times the belt pitch, so the pitch radius is that divided by two pi. Standard gravity is exactly 9.80665 m/s squared.
Motor torque context
- Force equals torque divided by pulley pitch radius; a smaller pulley gives more force.
- Holding torque is a data-sheet value at full current; it is not assumed here.
- Usable torque falls with speed and depends on driver voltage and current.
- Derate the static force result before relying on it for motion loads.
- A smaller pulley trades top speed for force by lowering travel per revolution.
Stepper motor torque: frequently asked questions
How does motor torque become linear force on a belt axis?
A pulley converts rotary torque into a tangential belt force. Force equals torque divided by the pulley pitch radius. The pitch radius equals the pulley tooth count times the belt pitch divided by two pi, because the pitch circumference is the teeth times the pitch.
Where do I find the holding torque?
Holding torque is a published specification on the motor's data sheet, usually in newton-centimeters, ounce-inches, or kilogram-force-centimeters. Enter it in newton-centimeters here, or convert first. This calculator does not assume a torque; you supply your motor's rating.
Is the usable torque the same as holding torque?
No. Holding torque is the static maximum at full current. Usable torque drops as speed rises and depends on driver voltage and current, so treat the force result as an upper bound that you derate for motion.
What is the pitch radius of a 20-tooth GT2 pulley?
With 20 teeth and a 2 mm pitch, the pitch circumference is 40 mm, so the pitch radius is 40 divided by two pi, about 6.366 mm. A smaller pulley produces more force for the same torque but less speed.
Why does a smaller pulley give more force?
Force is torque divided by radius, so reducing the radius increases the force for a fixed torque. The tradeoff is travel per revolution: a smaller pulley moves less belt per turn, which raises the steps per mm and lowers the top speed.
Official sources
- National Institute of Standards and Technology: Fundamental Physical Constants (standard gravity).
- RepRap project documentation: reprap.org (motion system reference).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.