Ball Screw Force Calculator

Compute axial force, torque demand, travel, and power. Model efficiency losses with responsive, easy inputs. See results above, export tables, and compare example values.

Calculator Inputs

Use SI-style units shown in each field label.

Jump to Example Table
Rotational torque driving one screw.
Linear travel for one full revolution.
Mechanical efficiency of the assembly.
Used for travel rate and power.
Assumes equal load sharing.
Design force equals force ÷ factor.
Optional. Used for torque demand checks.

Formula Used

This tool uses common ball screw energy relationships. Lead is converted from millimeters per revolution to meters per revolution before calculation.

Ideal axial force per screw: Fideal = (2π × T) ÷ Lead
Actual axial force per screw: Factual = (2π × T × η) ÷ Lead
Total available force: Ftotal = Factual × Number of Screws
Design force: Fdesign = Ftotal ÷ Safety Factor
Linear speed: v = (Lead × RPM) ÷ 60
Useful output power: P = Ftotal × v
Torque required per screw for a target load: T = (F × Lead) ÷ (2π × η)

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

  1. Enter the applied torque available at one screw.
  2. Enter the ball screw lead in millimeters per revolution.
  3. Enter estimated mechanical efficiency as a percentage.
  4. Add motor speed if you want travel rate and power outputs.
  5. Enter the number of screws sharing the axial load.
  6. Set a safety factor to reduce the force to a design value.
  7. Optionally enter a target axial load for torque demand checks.
  8. Press Calculate Force to display results above the form.
  9. 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.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.