Ball Screw Force Calculator

Turn torque into thrust with practical unit controls. Compare design force against motor capability. Download results and share them with your team.

Calculator
Inputs and options
Reset How to use
Use the first mode to check whether your motor can meet a target force.
This is the steady process load, excluding inertia.
Include payload plus carriage, nut, and attached components.
Use peak acceleration during ramps for a conservative design.
If unknown, start small and refine after testing.
Smaller lead increases mechanical advantage, but needs more revolutions.
0 to 1
Efficiency includes screw, nut, lubrication, and preload losses.
motor:screw
η_gear
If direct drive, ratio = 1 and η_gear = 1.
×
Accounts for uncertainties, peak events, and wear.
Enter continuous torque for a conservative estimate.
rpm
Used for linear speed and power estimates.
Higher precision helps debugging; lower precision improves readability.
Example data
Sample cases for quick testing

Tip: click Use to load a case into the form.

Use Case Load (N) Mass (kg) Accel (m/s²) Friction (N) Lead (mm/rev) η_screw Gear ratio η_gear SF Req. motor torque (N·m)
A 3500 120 0.8 150 10 0.9 8 0.97 1.25 1.07
B 1200 45 1.5 60 5 0.88 3 0.95 1.3 0.55
C 8000 200 0.4 250 20 0.92 10 0.97 1.2 3.57
D 400 25 2.2 40 8 0.85 3.2 0.97 1.4 0.33
E 2500 90 0.6 120 12 0.9 7.8 0.97 1.15 0.86
F 1500 30 3.0 80 25 0.88 5 0.95 1.1 1.75
G 6000 60 1.0 200 4 0.92 12 0.97 1.3 0.48
H 9800 150 0.2 300 16 0.9 9 0.97 1.25 4.10
These examples assume N, kg, m/s², and mm/rev. Adjust lead, efficiencies, and friction to match your hardware and lubrication.
Formula used
Core relationships

This calculator combines steady load, friction, and inertia:

  • F_inertia = m × a
  • F_base = F_load + F_friction + F_inertia
  • F_design = F_base × SF

Torque–thrust relationship for a screw drive:

  • F = (2π × T_screw × η) / lead
  • T_screw = (F × lead) / (2π × η)

Gearbox mapping (motor to screw):

  • T_screw = T_motor × ratio × η_gear
  • T_motor = T_screw / (ratio × η_gear)
Engineering note
Motor sizing also depends on duty cycle, screw critical speed, buckling, bearing loads, and thermal limits. Use this tool for first-pass force and torque checks.
How to use
Step-by-step guide
  1. Choose a mode: check thrust from torque, or size torque from thrust.
  2. Enter the external axial load in your preferred unit.
  3. Add moving mass and peak acceleration to include inertia.
  4. Estimate friction from guides, seals, and nut preload.
  5. Set lead and efficiency; use a preset if needed.
  6. Add gear ratio and gearbox efficiency for the drive train.
  7. Select a safety factor and press Calculate.
  8. Export results to CSV or PDF for documentation.
Tip: If your axis is vertical, include gravitational load inside the external axial load.

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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.