How this calculator works
A helical torsion spring bends its wire as its arms rotate. The ideal rate therefore uses Young modulus. Straight legs add bending compliance, represented here as equivalent active coils for perpendicular end loading. Inner-fibre curvature increases the bending stress. The model assumes elastic round wire, small geometric change and straight legs; bends, winding direction, coil contact and support friction can change performance. Body length is an unloaded geometric estimate using the entered inter-coil gap.
Formula
Ne=(l1+l2)/(3 pi D); Na=Nb+Ne; ktheta=E d⁴/(64 D Na); T=ktheta theta=F r. C=D/d; Ki=(4C²-C-1)/[4C(C-1)]; Ko=(4C²+C-1)/[4C(C+1)]; sigma_i=32 Ki T/(pi d³).
Worked example
With E=200 GPa, 2 mm wire, 20 mm mean diameter, 5 body coils and negligible leg flexibility, the rate is 0.5 N m/rad. A 0.5 N m torque produces 1 rad deflection; 0.5 rad requires 0.25 N m.
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Frequently asked questions
Why use Young modulus rather than shear modulus?
The dominant deformation in the coiled wire is bending even though the spring applies an external torque.
What happens when the legs get longer?
They add compliance and lower the overall angular rate under the stated loading model.
Does corrected stress give a fatigue life?
No. Compare stresses with material and duty-specific limits, including manufacturing condition and residual stresses.