Torsion spring calculator
Calculate the angular rate (per degree), maximum safe torque and maximum angle of torsion springs with legs.
Formula
M₃₆₀ is the torque for one full turn. Divided by 360 it becomes the angular rate per degree, the form the calculator displays.
Symbols
Worked example
Computed by the same engine as the calculator above, using the form's starting values.
Torsion springs store energy through rotation. The angular rate depends on the material's elastic modulus and the coil geometry.
Set the leg length and angle and see the available torque.
Always load the spring in the direction that winds the coil tighter: it seats the coils on the arbor and allows higher working stresses.
How to measure your spring
- Measure the wire diameter (d) on the body of the spring.
- Measure the outer diameter (OD) across the coils.
- Count the number of body coils.
- Measure the leg length from the body to the tip.
- Measure the free angle between the legs and note the wind direction (right or left hand). Torsion springs should be loaded in the direction that winds the coil tighter.
Material moduli and density
| Material | Shear modulus G | Elastic modulus E | Density |
|---|---|---|---|
| Carbon steel (MW) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Stainless 302 (SS302) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.90 g/cm³ |
| Stainless 17-7 (SS177) | 11.0 × 10⁶ psi (75.8 GPa) | 29.4 × 10⁶ psi (203.0 GPa) | 7.81 g/cm³ |
| Stainless 316 (SS316) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.98 g/cm³ |
| Oil tempered MB (OT) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Chrome silicon (CS) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Hard drawn (HD) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Phosphor bronze (PB) | 6.0 × 10⁶ psi (41.4 GPa) | 14.9 × 10⁶ psi (103.0 GPa) | 8.86 g/cm³ |
| Beryllium copper (BC) | 7.0 × 10⁶ psi (48.3 GPa) | 18.6 × 10⁶ psi (128.0 GPa) | 8.25 g/cm³ |
| Chrome vanadium (CV) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
Frequently asked questions
What units is a torsion spring rate measured in?
Torque per angle: lbf·in per degree in imperial or N·mm per degree in metric. Catalogs also quote the torque per full turn (360 degrees).
Does the direction of rotation matter?
Yes. The spring should be loaded in the wind direction, closing the coil. Loading it the other way opens the coils and drastically reduces the allowable load.
What changes the rate of a torsion spring?
Wire diameter (fourth power), mean diameter, number of coils and the material's elastic modulus. More coils or a larger diameter make the spring softer.
Design the spring and get an instant quote
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