Torsion Spring Rate
A helical torsion spring resists twisting rather than compression or extension, storing energy as it’s rotated about its axis. Its rotational spring rate can be derived from beam-bending theory for a coiled wire as k = Ed4 / (64Dn), where E is the material’s modulus of elasticity, d is wire diameter, D is mean coil diameter, and n is the number of coils, giving torque per radian of rotation.
The applied torque needed for a given angular deflection is then M = kθ. Torsion springs are used in clothespins, garage door mechanisms, and clipboards — anywhere a returning rotational force is needed. As with other spring types, wire diameter has the strongest effect on stiffness since it enters to the fourth power.
Last reviewed August 2026