Formula Used
Ideal thrust: F = 2πT / L
Usable thrust: F = 2πTη / L
Required torque: T = FL / 2πη
Lead angle: λ = atan(L / πdm)
Friction angle: φ = atan(μ)
Raising torque model: T = F[(dm / 2)tan(λ + φ) + μc(dc / 2)]
Here, T is torque, F is axial force, L is lead, η is efficiency, dm is mean screw diameter, μ is thread friction, μc is collar friction, and dc is collar diameter.
How to Use This Calculator
Enter the applied torque and screw lead first. Add an efficiency estimate when you know it. Use a lower efficiency for dry or heavily loaded screws.
Enter mean screw diameter and friction values for the advanced friction model. Add collar data when thrust bearing or washer friction is important.
Enter target force to estimate required torque. Add rpm to calculate linear speed and power. Press calculate. The result appears above the form and below the header.
Example Data Table
| Torque |
Lead |
Efficiency |
Ideal thrust |
Usable thrust |
| 5 N·m |
2 mm/rev |
35% |
15708 N |
5498 N |
| 12 N·m |
5 mm/rev |
45% |
15080 N |
6786 N |
| 20 N·m |
8 mm/rev |
30% |
15708 N |
4712 N |
Lead Screw Force Guide
A lead screw changes rotary torque into straight line thrust. The screw thread works like a wrapped incline. When torque turns the screw or nut, the load moves along the axis. The final force depends on torque, lead, efficiency, diameter, and friction. A small lead gives higher thrust. A larger lead gives more speed, but lower thrust for the same torque.
Why Force Changes
The ideal equation ignores losses. Real machines lose energy in thread sliding, bearings, seals, guides, and collars. That is why the same motor torque can produce different thrust in two assemblies. Efficiency is often the fastest way to include these losses. A careful design also checks friction directly. Thread friction depends on the lead angle and friction angle. Collar friction adds another torque demand when the load presses on a thrust washer or bearing face.
Using the Outputs
The calculator gives ideal thrust first. It then estimates usable thrust from efficiency. It also gives a friction based thrust when mean diameter, lead angle, and friction are supplied. Compare these values before choosing a motor. Use the lower practical value when safety matters. The required torque result helps when you already know the target force. The safety factored torque gives a margin for startup drag, contamination, wear, and misalignment.
Design Notes
Self locking is important for vertical loads. A screw is commonly self locking when the friction angle is greater than the lead angle. This condition can reduce back driving, but vibration can still move a system. Never rely on self locking alone for life safety. Use a brake, lock, or counterbalance when a falling load can cause harm.
Lead screws are useful in presses, jacks, gates, lifts, clamps, and positioning tables. They are simple and strong. They also create heat because sliding friction is high. Keep speed, duty cycle, lubrication, and material pairing in view. Check nut stress, screw buckling, critical speed, and end support before final selection. A force calculation is a starting point. A complete design also needs testing under real load. Record each assumption. Then compare calculated thrust with manufacturer ratings. This protects threads, bearings, motors, couplings, and nearby operators during repeated operation with documented safety margins for service.
FAQs
What is lead screw force?
Lead screw force is the axial thrust produced when torque turns a screw. It depends on torque, lead, efficiency, diameter, and friction. Lower lead usually gives more thrust from the same torque.
What is the basic force formula?
The ideal formula is F = 2πT / L. Real force is lower, so efficiency is added as F = 2πTη / L. This gives a practical estimate.
Why does efficiency matter?
Efficiency represents losses from sliding thread contact, bearings, guides, lubrication, and collars. A dry screw can have low efficiency. Ball screws usually have much higher efficiency than sliding lead screws.
What is screw lead?
Lead is the linear travel for one full revolution. It is not always the same as pitch. Multi-start screws move farther per turn because their lead equals pitch multiplied by starts.
What is lead angle?
Lead angle is the thread helix angle at the mean diameter. A higher lead angle increases speed, but it can reduce force and self-locking ability.
Can this calculator check back-driving?
Yes. It compares friction angle with lead angle. If friction angle is higher, the screw is more likely to self-lock. Still, vibration and wear can cause movement.
Does collar friction affect force?
Yes. Collar friction consumes extra torque when the load presses against a thrust collar or washer. The calculator adds this term in the friction model.
Should I use the ideal or friction result?
Use the friction or efficiency result for design. The ideal result is useful for comparison only. For real equipment, include safety factor, startup friction, misalignment, wear, and test data.