Helical Compression Spring Rate
Helical Compression Spring Rate
The stiffness of a round-wire helical compression spring is set by its wire diameter, coil diameter, number of active coils and material. This worksheet computes the spring rate and the deflection under a given load.
The spring rate is k = Gd⁴/(8D³n), where d is the wire diameter, D the mean coil diameter, n the number of active coils and G the shear modulus.
Inputs
G := 79 GPa=79000 MPa
d := 5 mm=5 mm
D := 40 mm=40 mm
n := 8=8
F := 200 N=200 N
Spring rate and deflection
k := G·d^4/(8·D^3·n)=12054.44 kg/s^2
x := F/k=16.59 mm
Results
The spring rate is the force needed per unit compression. Note the strong dependence on geometry: stiffness rises with the fourth power of wire diameter and falls with the cube of coil diameter, so small dimensional changes move the rate dramatically. Check that the deflection keeps the spring below its solid height.
Assumptions & limitations
- Round wire, constant pitch, linear (constant-rate) spring.
- Active coils only — exclude dead/ground end coils.
- Wahl curvature-stress correction not applied here (rate is unaffected; peak stress would need it).