A helical compression spring stores energy by twisting its wire as the coils squeeze together. Its spring rate — the force per unit of compression — comes from four things: how thick the wire is, how big the coils are, how many coils flex, and what the wire is made of. The standout is wire diameter, which enters to the fourth power: a tiny change in wire size swings the stiffness enormously. This calculator returns the rate, the force at any deflection you enter, the spring index, and the corrected shear stress so you can check the wire isn't overstressed.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Shigley / standard spring-design theory (Wahl factor).
The spring equations
The rate formula is exact for an ideal round-wire spring: stiffness grows with the fourth power of wire diameter and the first power of the shear modulus, and shrinks with the cube of coil diameter and the number of active coils. The Wahl factor Kw bumps up the nominal shear stress to account for the extra stress on the inside of each coil, which matters for fatigue life.
Worked example — a return spring
Scenario: A spring-steel spring with 2 mm wire, 16 mm mean coil diameter and 8 active coils, compressed 10 mm.
The spring needs about 48 N to compress 10 mm. Its index of 8 sits comfortably in the easy-to-coil 4–12 band. If this felt too soft, stepping the wire up to 2.2 mm — just 0.2 mm thicker — raises the rate to about 7.1 N/mm, nearly 50% stiffer, illustrating why wire diameter is the first thing to adjust when tuning a spring.
Frequently Asked Questions
The force needed to deflect a spring one unit of length (e.g. N/mm). A 5 N/mm spring needs 5 N per mm of travel. Higher rate = stiffer.
k = G·d⁴/(8·D³·Na): shear modulus, wire diameter (4th power), mean coil diameter (cubed) and active coils.
Rate scales with d⁴. 10% thicker wire (2.0→2.2 mm) is 1.1⁴ ≈ 1.46× stiffer — nearly 50% more.
~79.3 GPa (11.5 Mpsi) for carbon/alloy spring steel; ~69 GPa for stainless, making stainless springs slightly softer.
The coils that flex. Ground/closed end coils don't deflect; for squared-and-ground ends Na = total − 2.