Lead Screw Torque Calculator

Work out lead screw torque instantly with clear inputs, formula shown and shareable results.

About Lead Screw Torque Calculator

Lead screw torque combines the useful lifting component with thread friction: T = (F d/2)(tan(lambda) + mu)/(1 - mu tan(lambda)). Efficiency of an ACME screw is typically 20-40%, and if the backdriving torque comes out negative the screw is self-locking and will hold the load without brake.

Formula

Lead screw torque

T = (F x d/2) x (tan(lambda) + mu) / (1 - mu tan(lambda)), lambda = atan(lead / pi d)

Worked example

With the default values below, Lead Screw Torque Calculator returns Torque required of 1.38. Change any input above and every figure here is recalculated in your browser.

Inputs used

Axial load: 800 N
Screw lead: 5 mm/rev
Screw pitch diameter: 12 mm
Thread friction coefficient: 0.15

Results

Torque required: 1.38 N·m
Screw efficiency: 45.99% %
Backdriving torque: -0.08 N·m
Lead angle: 7.56 °

Step by step

1Values used
2Lead screw torque
3Torque required= 1.38 N·m
4Screw efficiency= 45.99 %
5Backdriving torque= -0.08 N·m
6Lead angle= 7.56 °

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When is a screw self-locking?

When the friction coefficient exceeds the tangent of the lead angle. Fine-pitch ACME screws usually are; ball screws almost never are.

Why use a ball screw instead?

Efficiency of 90% or more, so far less motor torque and heat. The trade is cost, backlash management and the need for a brake on vertical axes.