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Lead Screw Torque Calculator

Find how much torque a lead screw needs to move a given load.

Result

2.91 N·m

How it is calculated

The tool uses the simplified drive-torque relation T = (F × L) ÷ (2π × η). F is the axial load in newtons, L is the screw lead in millimetres (the travel per full turn, converted to metres inside the tool by dividing by 1000) and η is the mechanical efficiency as a fraction between 0 and 1. The output is torque in N·m, rounded to two decimals. Load and lead must be above zero, and efficiency must be above 0 and at most 1. A percentage such as 35 is rejected. The result covers the screw and nut only. It does not add bearing friction, motor acceleration, or any extra torque to start the load moving, so a safety margin is normally added on top.

Worked example

A screw has to push a load of 800 N. The lead is 8 mm and the efficiency is 0.35. Convert the lead to metres: 8 ÷ 1000 = 0.008 m. Work per turn: 800 × 0.008 = 6.4 N·m. Divide by 2π × 0.35 = 2.199: 6.4 ÷ 2.199 = 2.910. The tool shows 2.91 N·m. With a perfect efficiency of 1 the same load would need only 1.02 N·m, which shows how much the friction costs.

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Common mistakes

  • Confusing lead with pitch. Lead is the travel per revolution. On a multi-start screw lead is the pitch times the number of starts, so an 8 mm lead can come from a 2 mm pitch with 4 starts.
  • Entering efficiency as a percentage. 35 is rejected, and the correct entry is 0.35.
  • Typing the lead in inches or the load in kilograms-force. The tool expects millimetres and newtons, and a 80 kg load is about 785 N.
  • Using the ball-screw efficiency for a plain Acme thread, or the reverse. The torque differs several times between them.
  • Treating the result as the motor rating. It leaves out bearing friction, acceleration and a safety factor, so the motor needs a margin above it.

About this calculator

A lead screw converts rotational motion into linear motion, and the torque needed to drive it is calculated from the axial load, the screw’s lead (the linear distance traveled per revolution), and the mechanical efficiency of the thread — typically 20 to 40% for common Acme or trapezoidal threads because of friction between the screw and nut, versus 90%+ for a ball screw with rolling elements. The general relationship is T = (F × L) ÷ (2π × η), where F is the axial force, L is the lead, and η is efficiency.

Mechanical and mechatronics engineers use this calculation to size stepper or servo motors for CNC machines, 3D printers, linear actuators, and jack screws, since undersizing the motor means it stalls under load while oversizing wastes cost and power. It’s a standard step in the design of any linear-motion system built around threaded rod rather than a belt or ball screw.

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