Torsion Spring Deflection Angle Calculator
A torsion spring winds up by an angle proportional to torque: theta = T/k with the rate per turn set by wire, coil and material. The working torsion spring calculator returns the deflection angle, rate and corrected bending stress together.
Angle from torque
Torsion springs are linear in angle: the deflection is the applied moment over the angular rate.
theta = T / k_theta, k_theta ~ E*d^4 / (3667 * D * Na) [deg basis]
Stress is bending
Unlike compression springs, the wire bends: the inner-fibre stress uses the bending Wahl factor and the wire section modulus.
Body growth
Winding up reduces the coil diameter and lengthens the body - check arbor clearance at full deflection on the working calculator.
Frequently asked questions
Does deflection change the coil diameter?
Yes - winding in the load direction shrinks the body diameter and adds coils; the working calculator reports the deflected geometry for arbor clearance.
Which direction should a torsion spring be loaded?
In the wind-up direction. Unwinding loads the wire opposite its residual stresses and dramatically lowers the allowable.
Related pages
- Torsion spring calculator - deflection angle, rate per turn and corrected bending stress.
- Spring wire properties - E and allowable values by material.
- Spring index calculator - coil/wire proportions.