Actuator Holding Force and Back-Drive Calculator

Estimate screw lead angle, friction angle, self-locking margin, and idealized holding torque for a linear actuator screw drive. The result is a preliminary engineering estimate, not a product rating or safety approval.

Calculate holding torque and self-lock

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.

Screw lead angle --

Friction angle --

Self-locking angle margin --

Idealized holding torque estimate --

Enter values inside the documented model domain.

Engineering visualizer

Schematic, not to scale. The drawing updates from the production calculation engine and labels the main outputs.

Calculator by FIRGELLI Automations.

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When embedded on another page, the calculator shows only the working tool. FIRGELLI attribution, the visualizer, and the calculation-error report remain available.

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F = 1500 N, lead = 5 mm, d_m = 12 mm, μ = 0.15, η = 0.30. λ = 7.55°, φ = 8.53°, margin = 0.98° (barely self-locking). T_hold = 3.98 N·m. Wet or worn threads can wipe that margin.

What This Calculator Calculates

What does actuator holding force and back-drive 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 actuator holding force and back-drive 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 screw lead angle, friction angle, self-locking margin, and idealized holding torque for a linear actuator screw drive.

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
Screw lead angle	`lambda = atan(L/(pi d_m))`	Calculates screw lead angle for the stated simplified model.
Friction angle	`phi = atan(mu)`	Calculates friction angle for the stated simplified model.
Self-locking angle margin	`margin = phi - lambda`	Calculates self-locking angle margin for the stated simplified model.
Idealized holding torque estimate	`T_hold = F L/(2 pi eta)`	Calculates idealized holding torque estimate for the stated simplified model.

Variables and canonical units

Symbol	Variable	SI unit	Domain
`axial_load`	Axial load to hold	N	finite engineering value in the documented model domain
`screw_lead`	Screw lead per revolution	m	finite engineering value in the documented model domain
`mean_diameter`	Screw mean diameter	m	finite engineering value in the documented model domain
`friction_coefficient`	Thread friction coefficient	1	finite engineering value in the documented model domain
`screw_efficiency`	Screw efficiency estimate	1	finite engineering value in the documented model domain
`lead_angle`	Screw lead angle	rad	finite result from valid inputs
`friction_angle`	Friction angle	rad	finite result from valid inputs
`self_locking_margin`	Self-locking angle margin	rad	finite result from valid inputs
`ideal_holding_torque`	Idealized holding torque estimate	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 = 1500 N, lead = 5 mm, d_m = 12 mm, μ = 0.15, η = 0.30. λ = 7.55°, φ = 8.53°, margin = 0.98° (barely self-locking). T_hold = 3.98 N·m. Wet or worn threads can wipe that margin.

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: Screw lead-angle 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.

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Actuator Holding Force and Back-Drive Calculator