Torsional Spring Calculator

Torsional Spring Behavior

A torsional spring resists angular deflection. Within the elastic range, torque is proportional to twist angle. The spring rate $k$ has units of newton-meters per radian (N·m/rad).

Hooke's Law for Torsion

$$\tau = k \theta$$

Torque $\tau$ equals the spring rate times the deflection angle $\theta$ in radians. Convert degrees to radians: $\theta_{\mathrm{rad}} = \theta_{\mathrm{deg}} \times \pi / 180$.

Wire Spring Rate

$$k = \frac{G d^4}{64 n D^3}$$

For a helical torsion spring, $G$ is shear modulus (Pa), $d$ is wire diameter, $D$ is mean coil diameter, and $n$ is the number of active coils. This estimates $k$ from geometry before applying $\tau = k\theta$.

Related tools: Torsional Constant Calculator and Torque Calculator.

Frequently Asked Questions

What is the difference between torque and spring rate?

Spring rate $k$ is stiffness (N·m/rad). Torque $\tau$ is the actual twisting force produced at a given angle. Torque equals rate times angle.

Why must angle be in radians?

The torsion formula $\tau = k\theta$ requires $\theta$ in radians because $k$ is defined per radian of twist. Degrees must be converted first.

Where are torsional springs used?

Common applications include clothespins, mouse traps, door return mechanisms, and balance wheels in mechanical watches.

What shear modulus should I use for steel wire?

Carbon steel wire typically uses $G \approx 79$ GPa. Stainless steel is close to 75 GPa. Check material datasheets for precise values.

Does this calculator include stress limits?

No. It computes torque from linear elastic behavior. Verify that stress stays below the material yield point for your application.

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Torsional Spring

Torsional Spring Behavior

Hooke's Law for Torsion

Wire Spring Rate

Frequently Asked Questions

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