Capstan Belt Friction Calculator
Calculate the ideal limiting tight-side tension for a flexible line wrapped around a fixed surface.
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Result
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Calculation steps
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How to calculate
Use the Euler–Eytelwein capstan relation at impending relative slip.
Ttight/Tslack=exp(μθ), with θ in radians
Worked example
For100N slack-side tension, μ=0.3 and180° contact, limiting tension ratio≈2.56633240 and tight-side tension≈256.633240N. Zero friction gives equal tensions.
Assumptions and input details
Nonnegative slack tension, friction coefficient0–2, wrap0–3600 in the selected input unit, converted angle≤100rad and μθ≤100. Ideal flexible line, Coulomb static friction and fixed circular contact; ignore line stiffness, weight, centrifugal force and adhesion. Equality applies at impending slip, not every static state. The result is not a rope, lifting, braking or anchor rating.
References: Engineering Statics: flexible belt friction
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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