Torsion Spring Calculator

Inputs

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Diameter of the spring wire.
mm
Center-to-center across the coil (outside diameter − wire diameter).
mm
Number of active body coils that wind up under load.
coils
Torque applied about the coil axis to wind the spring.
N·m
Music wire ≈ 207 GPa, stainless ≈ 193 GPa.
GPa

Results

Default result
Edit inputs
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.

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