Lead Screw Torque Calculator

To pick a motor for a screw-driven axis, you need the torque it takes to move the load, and that depends on more than the weight: the screw's lead and its efficiency decide how much of the load the motor actually feels. This works out the torque to drive a lead screw or ball screw against a force, and adds the feed rate and the power if you give it a speed.

Lead and efficiency do the work

A screw is a ramp wrapped around a shaft, and the lead is how steep that ramp is: a bigger lead moves the axis farther per turn but asks for more torque to drive the same load. Efficiency is the other half. A plain ACME screw loses most of the turning effort to friction between the nut and the thread, so the motor feels far more than the raw load, while a ball screw rolls on bearings and keeps almost all of it. The torque is the load times the lead, divided by two pi and the efficiency.

Self-locking versus back-driving

The inefficiency of an ACME screw is not all bad. A screw that wastes enough to friction is self-locking: switch the motor off and the load stays put, because the load alone cannot turn the screw. That is why so many vertical lead-screw axes hold position with no power. A ball screw is efficient enough to back-drive, so a weight on a vertical ball screw will wind it down unless the motor holds it or a brake does. Factor that in before you put a heavy load on an efficient screw.

What the load force really is

On a vertical axis the load is the weight it lifts plus any cutting or pushing force, so a Z-axis carrying a spindle sees both. On a horizontal axis gravity drops out and the load is mostly the friction of the ways plus the cut, which is often much less. Use the real force the screw pushes against, not just the mass of the part, and remember that a cut adds to it. The torque scales straight with that force.

Size the motor above this

The torque here is the steady value to move the load at constant speed, with nothing to spare. A real motor needs margin: to accelerate the load up to speed, to cover stiction at the start, and to not run at its limit where a stepper loses steps. A common rule is to pick a motor with roughly double this torque at the speed you will run, since stepper torque drops as rpm climbs. Check the motor's torque at your actual speed, not just its holding figure.

More MakerKiln tools

• steps per mmSteps per mm CalculatorSteps per mm for a belt or lead-screw axis, and E-steps calibration.→
• gear ratioGear Ratio CalculatorReduction, output RPM and torque multiplication from two tooth counts.→
• pulley rpmPulley RPM CalculatorOutput RPM, drive ratio and torque change between two pulleys.→

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