created at July 12, 2022

# Coil Spring Stiffness

A coil spring is made by winding a wire around a cylinder. Here we consider a tension/extension or compression spring.

In the simplest case the spring has linear deformation curve (Hooke's law), so we can calculate the constant stiffness coefficient (N/m):

$k = \frac{G\cdot d^4}{8\cdot D^3 \cdot n}$

Where G - shear modulus, d = wire diameter, D - spring coil (measured by coil center line), n - number of coils. For spring steel the typical shear modulus value is 78.5 GPa.