Compute spring rate k = Gd⁴/(8D³Na), deflection, spring index, Wahl-corrected shear stress, and solid height for a round-wire helical compression spring.
Enter wire diameter, mean coil diameter, active coils, material, and force for rate, deflection, and stress.
About this tool
The Helical Compression Spring Calculator is a free, in-browser tool that computes the mechanical properties of a round-wire helical compression spring from its geometry and material. It returns the spring rate k = G·d⁴/(8·D³·Na), the deflection under a given force, the spring index, the Wahl-corrected shear stress, and the solid height. Enter the wire diameter d, the mean coil diameter D, the number of active coils Na, and the applied force F. Everything is computed locally in your browser.
The rate is k = G·d⁴/(8·D³·Na), where G is the material's shear modulus — music wire is about 79.3 GPa and stainless about 69 GPa, or you can enter a custom value. Deflection follows from Hooke's law as x = F/k. The spring index C = D/d describes the coil proportions, and the Wahl correction factor Kw = (4C − 1)/(4C − 4) + 0.615/C accounts for the extra stress on the inner coil surface, giving the peak shear stress τ = Kw·8·F·D/(π·d³). If you enter the total coil count Nt, the solid (fully-compressed) height is Ls = d·Nt. Work in SI (mm, N) with rate in N/mm and stress in MPa, or imperial (in, lbf) with rate in lbf/in and stress in psi.
As a worked example, a music-wire spring (G = 79.3 GPa) with d = 2 mm, D = 15 mm, and Na = 8 active coils has a rate k = 79,300 × 2⁴ / (8 × 15³ × 8) ≈ 5.87 N/mm, so a 50 N force compresses it about 8.5 mm. Its index C = 7.5 gives a Wahl factor near 1.20 and a corrected shear stress of roughly 285 MPa. Keep the working stress within the material's allowable to avoid set and fatigue.
Frequently asked questions
How is spring rate calculated?
The rate of a round-wire helical compression spring is k = G·d⁴/(8·D³·Na), where G is the shear modulus, d the wire diameter, D the mean coil diameter, and Na the number of active coils. Because rate scales with d⁴ and inversely with D³, small changes in wire or coil diameter shift stiffness sharply.
What is the spring index and Wahl factor?
The spring index C = D/d is the ratio of mean coil diameter to wire diameter, typically 4–12. The Wahl correction Kw = (4C − 1)/(4C − 4) + 0.615/C raises the nominal shear stress to account for curvature and direct shear on the inner coil surface, giving τ = Kw·8·F·D/(π·d³).
Which shear modulus should I use?
Use the material's shear modulus G: about 79.3 GPa (11.5 Mpsi) for music wire and hard-drawn carbon steel, and about 69 GPa (10 Mpsi) for 302/304 stainless. Pick the preset that matches your wire, or choose custom and enter G in GPa for other alloys.
What is solid height?
Solid height Ls is the length of the spring when fully compressed so the coils touch, calculated here as Ls = d·Nt from the wire diameter and total coil count Nt. It sets the minimum length and the maximum usable deflection; the spring must never be compressed below its solid height in service.