What is the lead screw lifting torque formula?

T = F × L / (2π × η), where F is the axial force, L is the lead (distance moved per revolution), and η is the mechanical efficiency (0–1).

What is the lead screw lowering torque formula?

For back-drivable screws, T = F × L × (1 − η) / (2π). A negative result means the screw is self-locking and no torque is needed to hold the load.

What is the rack-and-pinion torque formula?

T = F × r / η, where F is the tangential force and r is the pinion pitch radius. The result is the torque the motor must supply at the pinion shaft.

What efficiency value should I use?

Acme thread lead screws typically run 35–60% efficient; ball screws 85–95%; rack-and-pinion with spur gears 90–98%. Use the manufacturer spec when available.

What does back-drive mean?

A back-drivable lead screw will move under load when the motor is unpowered. This calculator flags screws as self-locking when η < 0.5 (tan(lead angle) < friction coefficient), meaning the load cannot back-drive the screw without a holding torque.

Payload Torque Calculator

Name: Payload Torque Calculator
Availability: InStock
Author: Nham Vu

Calculate the torque needed to move a payload with a lead screw or rack-and-pinion drive system.

Units:

Axial / Tangential Force (N)

Screw Lead (distance per revolution) (mm)

Mechanical Efficiency (%)

Acme screw: 35–60 % | Ball screw: 85–95 % | Rack & pinion: 90–98 %

Direction

Lifting Lowering

Enter values and click Calculate.

Lead screw lifting: T = F × L / (2π × η)

Lead screw lowering: T = F × L × (1 − η) / (2π) — negative means self-locking, no torque needed to hold.

Rack & pinion: T = F × r / η

F = force | L = lead per rev | r = pitch radius | η = efficiency (0–1)

Summary

Calculate the torque needed to move a payload with a lead screw or rack-and-pinion drive system.

How it works

Select the drive type — lead screw or rack-and-pinion.
Enter the payload force, drive geometry (lead or pitch radius), and mechanical efficiency.
For lead screws, choose lifting or lowering direction.
Click Calculate to see the required torque and the formula applied.
Toggle between SI (N, mm, N·m) and Imperial (lbf, in, in·lbf) units as needed.

Use cases

Size the motor for a CNC Z-axis or 3D printer lead screw.
Determine torque requirements for a rack-and-pinion linear slide.
Verify that a chosen stepper or servo motor can handle the load.
Check back-drive risk on a lead screw before omitting a brake.
Compare SI and Imperial torque values during machine design.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu