Calculator Inputs
Use SI-style units shown in each field label.
Formula Used
This tool uses common ball screw energy relationships. Lead is converted from millimeters per revolution to meters per revolution before calculation.
Where T is torque in N·m, Lead is meters per revolution, η is efficiency as a decimal, F is axial force in newtons, and v is linear speed in meters per second.
How to Use This Calculator
- Enter the applied torque available at one screw.
- Enter the ball screw lead in millimeters per revolution.
- Enter estimated mechanical efficiency as a percentage.
- Add motor speed if you want travel rate and power outputs.
- Enter the number of screws sharing the axial load.
- Set a safety factor to reduce the force to a design value.
- Optionally enter a target axial load for torque demand checks.
- Press Calculate Force to display results above the form.
- Use the CSV or PDF buttons to export the results.
Example Data Table
These sample rows show how force and speed change with torque, lead, efficiency, and screw count.
| Torque (N·m) | Lead (mm/rev) | Efficiency (%) | RPM | Screws | Actual Force per Screw (N) | Design Force (N) | Travel Rate (m/min) |
|---|---|---|---|---|---|---|---|
| 2.00 | 5.00 | 88.00 | 900 | 1 | 2,211.68 | 1,701.29 | 4.500 |
| 3.50 | 10.00 | 90.00 | 1,200 | 1 | 1,979.20 | 1,319.47 | 12.000 |
| 5.00 | 20.00 | 92.00 | 1,500 | 2 | 1,445.13 | 1,651.58 | 30.000 |
Frequently Asked Questions
1) What does this ball screw force calculator estimate?
It estimates axial force from torque, lead, and efficiency. It also calculates travel speed, useful output power, total force for multiple screws, and a reduced design force using your chosen safety factor.
2) Why does higher lead usually reduce axial force?
For the same torque, a larger lead moves the nut farther each revolution. That increases travel rate, but it reduces mechanical advantage, so axial force falls unless torque increases too.
3) Why is efficiency included in the formula?
Efficiency accounts for friction and mechanical losses. Ideal force assumes perfect conversion. Actual force multiplies the ideal value by efficiency, giving a more realistic estimate for practical use.
4) What units should I enter?
Use torque in newton-meters, lead in millimeters per revolution, speed in RPM, and load in newtons. The calculator converts lead internally and reports speed in meters per second and meters per minute.
5) What does design force mean here?
Design force is the total available force divided by your safety factor. It is a conservative value used for planning, allowing margin for uncertainty, wear, uneven loading, and dynamic effects.
6) Can I use this for multiple ball screws?
Yes. Enter the number of screws sharing the same load. The tool assumes equal load distribution across screws, which is reasonable only when alignment, stiffness, and mounting conditions are similar.
7) Does this tool replace detailed machine design?
No. It is a fast estimation tool. Detailed design should also check column strength, buckling, critical speed, bearing loads, duty cycle, shock loading, lubrication, mounting rigidity, and manufacturer ratings.
8) Can a ball screw hold a vertical load without backdriving?
Not always. Many ball screws are highly efficient and can backdrive under load. Vertical systems often need a brake, counterbalance, or locking method if load holding is required during power loss.