Actuator Position Error Budget Calculator

Posted by Robbie Dickson on

Actuator Position Error Budget Calculator

Combine backlash, lead error, feedback quantization, repeatability, compliance, and thermal growth into bounded and RSS actuator-axis position-error estimates. The result is a preliminary engineering estimate, not a product rating or safety approval.

Calculate the position error budget

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.

mm
Enter directional backlash allowance for the modeled condition.
mm
Enter lead or travel error for the modeled condition.
mm
Enter feedback quantization for the modeled condition.
mm
Enter repeatability contribution for the modeled condition.
mm
Enter mounting or compliance contribution for the modeled condition.
mm
Enter thermal position shift for the modeled condition.
Arithmetic bounded position-error estimate --
RSS combined standard-position uncertainty estimate --
Bidirectional backlash deadband --
Enter values inside the documented model domain.

Engineering visualizer

Actuator Position Error Budget Calculator visualizer Schematic, not to scale. The drawing updates from the production calculation engine and labels the main outputs.

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

Calculator by FIRGELLI Automations.

Embed this calculator

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

What This Calculator Calculates

What does actuator position error budget 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.

How To Interpret The Results

How should I interpret the actuator position error budget result? A larger result means the checked effect is becoming more important and should be compared with product data, mounting limits, or the next design check. A smaller result does not prove the whole system is safe.

When Not To Use This Calculator

When should I not use the actuator position error budget 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

Combine backlash, lead error, feedback quantization, repeatability, compliance, and thermal growth into bounded and RSS actuator-axis position-error estimates.

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
Arithmetic bounded position-error estimate E_bound = sum |e_i| Calculates arithmetic bounded position-error estimate for the stated simplified model.
RSS combined standard-position uncertainty estimate E_RSS = sqrt(sum e_i^2) Calculates rss combined standard-position uncertainty estimate for the stated simplified model.
Bidirectional backlash deadband D_backlash = 2b Calculates bidirectional backlash deadband for the stated simplified model.

Variables and canonical units

Symbol Variable SI unit Domain
backlash Directional backlash allowance m finite engineering value in the documented model domain
lead_error Lead or travel error m finite engineering value in the documented model domain
feedback_quantization Feedback quantization m finite engineering value in the documented model domain
repeatability Repeatability contribution m finite engineering value in the documented model domain
mounting_compliance Mounting or compliance contribution m finite engineering value in the documented model domain
thermal_shift Thermal position shift m finite engineering value in the documented model domain
bounded_error Arithmetic bounded position-error estimate m finite result from valid inputs
rss_error RSS combined standard-position uncertainty estimate m finite result from valid inputs
bidirectional_deadband Bidirectional backlash deadband 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

b = 0.20 mm, lead 0.10, q 0.05, r 0.08, compliance 0.15, thermal 0.12. E_bound = 0.70 mm. E_RSS = 0.309 mm (all six). Deadband D = 0.40 mm. RSS includes b (unlike the backlash sibling). Do not 301 to the backlash page.

Related checks: backlash and position error budget, potentiometer position accuracy calculator, Hall-sensor position resolution calculator.

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

  1. 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.
  2. 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.

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: Linear-axis bounded and RSS position-error budget

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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Use the result to select and verify an actuator

Use the result as a starting point. Add a suitable safety margin, then check the real mechanism and the exact product data before choosing an actuator.

  1. 1. Record the requirementKeep the result with its units, input conditions, assumptions and safety factor.
  2. 2. Compare product familiesScreen force, stroke, loaded speed, voltage, dimensions, mounting, feedback, duty cycle and environment.
  3. 3. Verify the exact SKUCheck the current product page, performance evidence and technical drawing before release or purchase.

One calculated value is not enough to select an actuator. Check mounting geometry, side and shock loads, loaded speed, power and control requirements, duty cycle, temperature, and environmental exposure. Test the complete mechanism where a failure could cause injury or expensive damage.