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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 Diamter
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

Disclaimer - We don't guarantee the accuracy of this calculator.

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

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


These equations come from the Wiki article on force.

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

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