Torsion Spring Calculator

Inputs

Wire diameter (d)

Diameter of the spring wire.

Mean coil diameter (D)

Center-to-center across the coil (outside diameter − wire diameter).

Active coils (Nₐ)

Number of active body coils that wind up under load.

coils

Applied moment (M)

Torque applied about the coil axis to wind the spring.

N·m

Young's modulus (E)

Music wire ≈ 207 GPa, stainless ≈ 193 GPa.

GPa

Default result

Deflection angle(θ)

140.9°

Wind-up under the applied moment.

Also computed

Max bending stress(σ)1,376MPa

At the inner fibre of the wire.

Spring index(C)10

Rate per turn(R)2.556N·m

Moment per 360° turn.

Method notes 4 notes

A torsion spring is loaded in bending, so the rate uses Young’s modulus E (not the shear modulus G) and the bending Wahl factor Kb (not the shear Kᵥᵥ of a compression spring).
Rate per turn R = E·d⁴ / (10.8·D·Nₐ); the deflection is the applied moment divided by the rate, in turns.
The peak bending stress σ = Kb · 32·M / (π·d³) occurs at the inner fibre of the wire; as the spring winds up the body coils tighten and the inside diameter shrinks.
Static load; ignores fatigue, set and stress relaxation. The arm leverage and end effects are not modelled.