How to calculate a compression spring
Learn to calculate spring index, spring rate, stress and solid height of a compression spring — with the formulas engineers use.
A compression spring is defined by a handful of parameters: wire diameter (d), outer diameter (OD), free length (FL), number of coils and material. From these you can calculate the spring's entire behaviour.
Spring index
The index C relates the mean diameter (D = OD − d) to the wire diameter. Values between 4.5 and 12 are ideal for manufacturing; outside 4.5–25 the spring usually isn't manufacturable.
Spring rate
The spring rate k tells you how many newtons are needed to compress the spring by 1 mm. It depends on the material's shear modulus G, the wire diameter and the number of active coils (Na).
Stress and the Wahl factor
The shear stress in the wire sets the maximum safe load. The Wahl factor (Kw) corrects for the stress concentration on the inner side of the coil.
Solid height and manufacturing limits
Solid height is the length of the fully compressed spring (about d × number of coils for closed & ground ends). Free length must always exceed solid height, and pitch should not exceed 12 times the wire diameter.
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