Torsion Spring Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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When you need a quick torsion spring check, the best result is one you can explain, not just copy. Mechanical systems combine geometry, speed, force, losses, and material limits, so a quick equation is best treated as a transparent first model. The calculator below uses a narrow equation set and shows the output in a form that is easy to sanity-check.

What this calculator does

This page focuses on torsion spring rate from Spring diameter (D), Wire diameter (d), Number of active turns (Nₐ). The calculation stays deliberately narrow: it uses the fields tied to this relationship and reports related quantities only when they follow from those same inputs.

How to use it

Enter Spring diameter (D), Wire diameter (d), Number of active turns (Nₐ), Young modulus (E), Applied force (F) from the same physical setup, keeping every unit consistent with the selector shown on the page. After the result appears, make one small input change as a sanity check rather than relying on the first number simply because it has several decimal places.

How the calculation works

The page computes spring index C = D/d, correction factors from C, applied torque M = Fr, and bending stress 32KiM/(πd³). Its torsion-spring rate is k = Ed⁴/(10.8DN), with torque at the selected angle shown as kθ.

Example

Using the default example on the page (Spring diameter (D) = 20 mm; Wire diameter (d) = 2 mm; Number of active turns (Nₐ) = 5; Young modulus (E) = 200 GPa), the calculator returns torsion spring rate of 2.962963 N·m/rad. Try increasing one input while holding the others fixed; the response should match the dependence shown in the formula above.

How to interpret the result

The torsion spring rate is best used as a baseline under the same operating assumptions. When comparing scenarios, keep the unit system and definition of RPM, diameter, efficiency, pressure, force, or ratio unchanged so the difference reflects the input you intended to test.

Limitations and notes

The formula is a simplified round-wire torsion-spring model. End-leg geometry, initial tension, coil friction/contact, nonlinear large-angle effects, fatigue, and material limits are not evaluated. Confirm units carefully because d enters to the fourth power.