How this calculator works
A close-coiled axial spring stores energy mainly by twisting its wire, so its rate depends on shear modulus. A helical torsion spring bends its wire and uses Young modulus instead. Both formulas assume round wire, small elastic deflection and a constant mean diameter. Axial load is a magnitude with no preload; extension springs with initial tension need that added separately. Compression free and solid lengths are approximate end-geometry estimates, not extension-hook dimensions. For torsion, enter an effective active count or select body coils and straight leg lengths to include their compliance. In body mode the coil-count inverse reports both body and effective counts.
Formula
Axial: k=G d⁴/(8 D³ Na), F=k x. Torsion: ktheta=E d⁴/(64 D Na), T=ktheta theta; Na=Nb+(l1+l2)/(3 pi D) for the straight-leg option. Spring index C=D/d; outside diameter=D+d.
Worked example
With G=80 GPa, 1 mm wire, 10 mm mean diameter and 10 active coils, axial rate is 1000 N/m and 10 mm deflection requires 10 N. A torsion spring with E=200 GPa, 2 mm wire, 20 mm mean diameter and 5 active coils has rate 0.5 N m/rad.
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Frequently asked questions
Why are the material moduli different?
Axial helical springs mainly twist the wire; helical torsion springs mainly bend it.
Does this include an extension spring's initial tension?
No. Add measured initial tension to k times extension after the coils separate.
Does the tool predict spring life?
No. Stress, fatigue, coil contact, buckling and manufacturing tolerances need separate checks.