Lead Angle & Lead Screw Torque Calculator

About the Lead Angle & Lead Screw Torque Calculator

The Lead Angle & Lead Screw Torque Calculator determines the lead angle, required driving torque, efficiency, and self-locking behavior of power screws - ACME, ball screws, and trapezoidal threads. It is useful in machine design, linear actuators, screw jacks, and CNC lead screw selection because these systems trade speed, force, and backdrive resistance.

The lead angle is the angle between the helix of the thread and a plane perpendicular to the axis. It directly affects torque requirements, efficiency, and whether the screw is self-locking, meaning it will not backdrive under load. Most ACME screws with friction coefficients above 0.15 are self-locking at lead angles below about 5°.

Enter the lead, pitch diameter, thread angle, friction coefficient, and axial load. The calculator shows the required torque to raise and lower the load, mechanical advantage, efficiency, and critical backdrive analysis, so you can compare ACME, ball, and buttress thread profiles side by side before sizing a motor or choosing a screw type.

When This Page Helps

Use this calculator when you need to connect lead, friction, and pitch diameter to real drive torque and backdrive behavior instead of relying on rough screw-jack rules of thumb. It is useful for actuator sizing, vertical-load checks, and comparing when ACME or ball screws make more sense before you commit to hardware.

How to Use the Inputs

1. Enter the screw lead (axial distance per revolution).
2. Enter the pitch diameter (mean thread diameter).
3. Enter the thread half-angle (ACME = 14.5°, ball = 0°).
4. Enter or select the friction coefficient.
5. Enter the axial load to be raised.
6. View lead angle, torque, efficiency, and self-locking status.
7. Compare screw types using the reference table.

Example Calculation

Tips & Best Practices

• Multi-start screws increase lead without increasing pitch — faster travel, same thread engagement.
• Always include a safety factor of 1.5-2× on self-locking analysis for vertical load applications.
• Collar friction (thrust bearing) can add 20-50% to the total torque — account for it in motor sizing.
• Ball screws require a brake or worm gear to prevent backdriving in vertical applications.
• Start with ACME for prototypes (cheaper, self-locking), switch to ball screws if efficiency matters.

Thread Profile Comparison

ACME threads have a 29° included angle (14.5° half-angle). This trapezoidal shape is easy to machine and provides good strength. Efficiency ranges from 25-40% depending on friction and lead angle.

Ball screws replace sliding friction with rolling contact via recirculating ball bearings. Efficiency exceeds 90%, but they require external braking for vertical loads and cost significantly more.

Buttress threads (7° load face, 45° clearance face) are optimized for one-direction loading — ideal for vises, presses, and jack screws where the load is always compressive.

Self-Locking Design Guidelines

Self-locking is not a binary property — it depends on friction, which varies with lubrication, temperature, vibration, and wear. OSHA and ASME standards require a mechanical brake or nut lock for safety-critical vertical lifts even if the screw theoretically self-locks.

The rule of thumb: a screw is reliably self-locking when μ > 1.5 × tan(λ) × cos(α). This provides a 50% safety margin against dynamic friction reduction.

Motor Sizing for Lead Screws

Total motor torque = raising torque + acceleration torque + collar friction torque. For continuous duty, the motor rating should be ≥1.25× the total steady-state torque. For intermittent duty with frequent starts/stops, account for inertia of the screw and load.

Frequently Asked Questions

• What is the lead angle?

  The lead angle (λ) is the angle the thread helix makes with a plane perpendicular to the screw axis. It equals atan(lead / (π × pitch diameter)). Higher lead angles mean faster travel but require more torque.

• When is a screw self-locking?

  A screw is self-locking when it won't backdrive under load. This occurs when the friction coefficient (μ) exceeds tan(λ)×cos(α). Practically, ACME screws with μ ≥ 0.15 and lead angles below ~6° are reliably self-locking.

• What is the difference between lead and pitch?

  Pitch is the distance between adjacent threads. Lead is the axial distance per revolution. For single-start threads, lead = pitch. For multi-start: lead = pitch × number of starts.

• ACME vs ball screw — which is better?

  Ball screws have 90%+ efficiency vs 25-40% for ACME, but are not self-locking and cost 5-10× more. ACME is preferred for vertical loads, lifting, and cost-sensitive applications. Ball screws for CNC, robotics, and precision motion.

• What friction coefficient should I use?

  Steel on bronze (lubricated): 0.08-0.12. Steel on steel (lubricated): 0.10-0.15. Steel on steel (dry): 0.15-0.25. Ball screw: 0.003-0.01. PTFE-coated: 0.04-0.08. Pick the value that best matches the actual material pair and lubrication state, because that choice has a large effect on torque and self-locking behavior.

• How do I increase lead screw efficiency?

  Use a larger lead angle (multi-start threads), reduce friction (better lubrication, PTFE coatings, ball screws), or reduce collar friction with thrust bearings. Note: higher efficiency means less self-locking ability.