Lead Screw Torque and Force Calculator

When designing machinery that uses lead screws, it's a common task to try and figure out the size of motor needed to drive a given force with a lead screw. This calculator will calculate torque given the lead screw parameters and the required force.

There are two torques the torque to raise the load and the torque to lower the load.

Once the torque is calculated an appropriate stepper can be selected.

Common Stepper Motor Typical Torque Ranges and Dimensions
Motor	Torque in N*cm	Dimensions	Shaft Diameter
NEMA 8	4	20mm sq	4mm,5mm
NEMA 11	11-13	27mmx sq	5mm
NEMA 14	9-15	35mmx sq	5mm
NEMA 17	44-54	42mmx sq	5mm
NEMA 23	180-300	57mmx sq	0.25 in
NEMA 34	200-1100	86mmx sq	14mm

Input
Force	lb oz g N
Pitch Diameter	in mm
Thread density	Threads per in cm
Coefficient of Friction	(See table below)
Result Units	N*m N*cm lb*in oz*in
Result
Torque (Raise)	(Selected Units)
Torque (Lower)	(Selected Units)

Coefficient of Friction for Leadscrew Threads

Screw Material	Nut material
	Steel	Bronze	Brass	Cast iron
Steel, dry	0.15 - 0.25	0.15 - 0.23	0.15 - 0.19	0.15 - 0.25
Steel, machine oil	0.11 - 0.17	0.10 - 0.16	0.10 - 0.15	0.11 - 0.17
Bronze	0.08 - 0.12	0.04 - 0.06	-	0.06 - 0.09

Equations:

These equations come from the Wiki article on force.

Torque(raise) = F*Dm/2*(L+u*PI*DM)/(PI*Dm-u*L)

Torque(lower)= F*Dm/2*(L-u*PI*DM)/(PI*Dm+u*L)