EngineerBenchCalculating compression-spring rate
The spring-rate model uses wire diameter, mean coil diameter, active coils, and shear modulus. Mean coil diameter is measured through the center of the wire, not across the outside of the spring. Wire diameter has a fourth-power effect in the formula, so small dimensional changes can strongly affect rate.
Active coils and total coils are different
Active coils contribute to the working deflection. Total coils are used here to approximate solid height. The spring's end style affects both, so check the manufactured geometry. Working load divided by rate gives the modeled deflection from free length.
Check stress and remaining travel
The corrected shear stress includes a Wahl factor, while the distance-to-solid result checks the entered working point against the approximate solid height. Neither establishes fatigue life, stability against buckling, or a complete material selection. A spring can pass a static stress check and still be unsuitable for repeated service.
Relating spring rate to the working point
Spring rate is force change per unit deflection in the linear model. A spring rated at 20 N/mm deflects 10 mm under an added 200 N if that linear relationship applies over the travel. Free length minus working deflection gives the modeled loaded length. Compare that length with the approximate solid height rather than looking only at the stress result.
Wire diameter has a fourth-power influence on the rate equation, while mean coil diameter has a third-power influence in the denominator. Changing geometry therefore affects rate and stress in different ways. Count active coils according to the end arrangement, and do not treat all turns as active by default. The Wahl correction accounts for curvature-related stress effects in the represented helical-spring model; it does not establish a fatigue limit. Check available travel with allowance for manufacturing variation and the actual installation. A long slender spring may need guidance or a separate stability check even when its calculated stress and distance to solid appear acceptable.
Formula
k = Gd⁴/(8D³Na); Wahl factor corrects nominal torsional stress. Solid height approximated by total coils × wire diameter.