SpecCalcsReference calculators for the shop floor

Spring Rate Calculator

A music-wire spring with d = 2 mm wire, D = 16 mm mean coil diameter and 8 active coils has a rate of 4.84 N/mm, a spring index of 8, and a Wahl factor of 1.184. At 5 mm deflection it exerts 24.2 N.

Compression spring
Spring rate, k (N/mm)4.84
Spring index, C8
Wahl factor, KW1.184
Force at deflection (N)24.2

The formulas

Spring rate
k=Gd48D3Nak = \frac{G d^4}{8 D^3 N_a}
Wahl correction factor
KW=4C−14C−4+0.615CK_W = \frac{4C - 1}{4C - 4} + \frac{0.615}{C}
G shear modulus · d wire diameter · D mean coil diameter · Na active coils · C = D/d (spring index)

Spring index

The spring index C = D/d is the ratio of mean coil diameter to wire diameter. Values between 4 and 12 are considered practical — below 4 the spring is difficult to coil and the inner-fibre stress concentration is severe; above 12 the coils are loose and the spring may tangle or buckle. Most stock springs fall in the 6–10 range.

Wahl correction factor

The simple torsion formula for coil stress assumes the wire is straight. In reality the curvature of the coil raises the stress on the inner fibre. The Wahl factor KW corrects for both curvature and direct shear; it approaches 1.0 as the spring index increases (nearly straight wire) and exceeds 1.5 for tightly wound springs (C < 4). Corrected stress is τ = KW×8FD/(πd³).

Material selection

Music wire (ASTM A228) is the most common choice for small to medium springs — highest tensile strength, good fatigue life, low cost. Chrome vanadium and chrome silicon handle higher temperatures and shock loads. Stainless 302/304 is used where corrosion resistance matters but at a lower shear modulus (lower rate for the same geometry). Phosphor bronze and beryllium copper are chosen for electrical conductivity or non-magnetic requirements.