ExactBench · Engineering calculators

Lead Screw Calculator

Power screw · Shigley

Screw and load

Torque to raise

0.720
N·m
44.2 % efficient · lead angle 7.26°

Thread geometry

self-locking
ONE TURN, UNWRAPPEDloadcircumference π·dm = 31.42 mmlead 4.00 mmλ = 7.26°
Torque to lower0.0677 N·m
Efficiency44.22 %
Lead angle7.256°
Mean diameter10.000 mm
Self-lockingYes — holds under friction
Linear speed20.00 mm/s
Drive power22.6 W
How this is calculated. A screw thread is an inclined plane wrapped round a cylinder: one turn advances the load by the lead while travelling π·dm around. Shigley's relation gives the raising torque as T = (F·dm/2)·(l + πμdmsecα) / (πdm − μl·secα), where α is the thread half-angle — zero for a square thread, 14.5° for ACME, which wedges the nut and effectively increases friction. Efficiency is the useful work F·l over the work actually put in, 2πT, and for a typical ACME screw that lands around 20–40 %: most of your motor's effort becomes heat in the nut, which is exactly why ball screws exist. The same friction is what makes the screw self-locking — if πμdmsecα > l, the load cannot drive the screw backwards and a vertical axis stays up when the power is off. Efficient screws are not self-locking, and you cannot have both. Collar or thrust-bearing friction is not included here and adds to the total.
This screw is not self-locking — the load can back-drive it. On a vertical axis it will drop when the motor is unpowered unless you add a brake.