Ball Screw Back-Drive Torque Calculator
Estimate back-drive torque and holding torque from axial load, screw lead, and screw efficiency. The result is a preliminary engineering estimate, not a product rating or safety approval.
Calculate ball-screw back-drive torque
Enter the measured or assumed inputs in one unit system. The calculator converts to SI internally, evaluates the stated model, and displays the result in the selected unit system.
Engineering visualizer
Schematic, not to scale. The drawing updates from the production calculation engine and labels the main outputs.
Calculator by FIRGELLI Automations.
Embed this calculator
The responsive iframe opens the calculator-only view without Shopify navigation or footer. FIRGELLI attribution, the visualizer, and calculation-error reporting remain available.
F = 2000 N, lead = 5 mm, η = 0.90. T_back = 1.43 N·m. T_hold = 1.77 N·m. High efficiency is why a brake is usually required on a vertical ball screw.
Related checks: holding force and back-drive calculator, screw efficiency and required torque calculator, and industrial actuators.
What This Calculator Calculates
What does ball screw back-drive torque mean? This quantity describes one specific part of the actuator design problem. It should be read as a model output, not as a complete product selection rule.
When Not To Use This Calculator
When should I not use the ball screw back-drive torque model? Do not use this model when the inputs are unknown, the mechanism is outside the stated boundary, or the decision depends on manufacturer ratings, fatigue, shock, compliance, or regulated safety approval.
Engineering model and calculation details
Estimate back-drive torque and holding torque from axial load, screw lead, and screw efficiency.
The page separates the calculator result from product selection. It explains the inputs, limitations, interpretation, and next design checks so the result is not mistaken for a complete actuator rating.
Governing equations
| Quantity | Equation | Model meaning |
|---|---|---|
| Idealized back-drive torque | T_back = F lead eta/(2pi) |
Calculates idealized back-drive torque for the stated simplified model. |
| Idealized holding torque without brake margin | T_hold = F lead/(2pi eta) |
Calculates idealized holding torque without brake margin for the stated simplified model. |
Variables and canonical units
| Symbol | Variable | SI unit | Domain |
|---|---|---|---|
axial_load |
Axial load | N | finite engineering value in the documented model domain |
screw_lead |
Screw lead per revolution | m | finite engineering value in the documented model domain |
screw_efficiency |
Screw efficiency | 1 | finite engineering value in the documented model domain |
backdrive_torque |
Idealized back-drive torque | N_m | finite result from valid inputs |
holding_torque |
Idealized holding torque without brake margin | N_m | finite result from valid inputs |
Assumptions and boundary conditions
- Inputs represent one consistent operating condition.
- The model uses the simplified boundary stated on the page.
- The model begins and ends at the user-defined actuator or mechanism boundary.
Limitations and omitted checks
- The result depends on user-entered values and simplified boundary conditions.
- The model does not replace FIRGELLI product data, installation review, endurance testing, or a qualified engineering review.
- Shock, fatigue, misalignment, mounting strength, and controller behavior may govern before the calculated value.
Worked example
F = 2000 N, lead = 5 mm, η = 0.90. T_back = 1.43 N·m. T_hold = 1.77 N·m. High efficiency is why a brake is usually required on a vertical ball screw.
Related checks: holding force and back-drive calculator, screw efficiency and required torque calculator, and industrial actuators.
What this model evaluates
| Mode or effect | Status | Disclosure |
|---|---|---|
| calculated quantity | evaluated | The named output is evaluated for the stated model. |
| manufacturer rating | not evaluated | The result is not a manufacturer product rating. |
| installation detail | not evaluated | Mounting, alignment, shock, fatigue, and environment require separate review. |
Common mistakes
- Treating a simplified estimate as a manufacturer rating.
- Mixing units or entering values measured at a different operating point.
- Ignoring mounting, alignment, shock, duty cycle, or controller limitations.
- Failing to compare the result with the next logical FIRGELLI design check.
Engineering references
- National Institute of Standards and Technology. NIST Guide to the SI. National Institute of Standards and Technology, Accessed 2026. Supports: SI unit definitions and unit-consistent engineering calculation display.. Accessed 2026-07-28. Source.
- Barry N. Taylor and Chris E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. National Institute of Standards and Technology, NIST Technical Note 1297. Supports: Root-sum-square treatment of independent standard uncertainty components.. Accessed 2026-07-28. Source.
Author, validation, and review status
Author: Robbie Dickson
Author profile: Robbie Dickson prepares FIRGELLI actuator education and calculator content for product users and engineering teams.
Engineering model type: Ball screw load to back-drive and holding torque estimate
Validation: The production JavaScript engine is compared with a separately written Python oracle across known-answer, SI/imperial-equivalent, boundary, invalid-input, and randomized cases.
Questions about this calculator or found an error? Message our engineering team.
