Conical spring

Deflection, stiffness and shear stress of a helical conical (tapered-coil) spring, from wire diameter and top/bottom mean coil diameters.

✓ validated against legacyoriginal: /calculators/t14_3.htm

Diameter of spring wire, d10⁻³ mMean coil diameter, 2r₁10⁻³ mMean coil diameter, 2r₀10⁻³ mNumber of active coils, nShear modulus, G = E/(2(1+ν))10⁹ PaSpring force, FN

Spring length closed, L_c = nd60 10⁻³ m

Spring deflection, f56.14 10⁻³ m

Spring stiffness, k = dF/df = F/f1.78 10³ N/m

Free spring length, L0 > L_c + f116.14 10⁻³ m

Pitch of lead, s = L0/n3.87 10⁻³ m

Shear stress, τ572.96 10⁶ Pa

Method & references

Helical conical (tapered-coil) spring — deflection, stiffness and shear stress based on the larger coil radius.

The computation is a literal port of the original client-side JavaScript from /calculators/t14_3.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Conical spring — Engineering ABC