➿ Helical Spring Calculator

A helical spring stores energy by twisting its wire. The spring rate—how many newtons it takes to compress it one millimeter—is set by four parameters: wire diameter, mean coil diameter, number of active coils and the shear modulus of the material. The helical spring calculator applies the standard design formula k = G·d⁴ / (8·D³·N), where G is the shear modulus, d the wire diameter, D the mean coil diameter and N the number of active coils.

The formula is famously sensitive: wire diameter enters to the fourth power, so a 10% thicker wire stiffens the spring by 46%. Coil diameter enters cubed, so spreading the coils 10% wider softens it by about 25%. That is why a small design change has an outsized effect—and why spring designers calculate before they wind. For a load of F, the deflection is δ = F / k and the wire stress can be estimated with the Wahl correction, which accounts for the curvature and direct shear that a simple torsion formula misses.

Shear stress in a loaded spring is highest at the inner surface of the coil, where the curvature concentrates it. The simple torsion stress τ = 8FD/(πd³) underestimates the true stress, so designers multiply by the Wahl factor Kₔ = (4C − 1)/(4C − 4) + 0.615/C, where C = D/d is the spring index. Springs with a small index (tight coils relative to wire) have a high Wahl factor and fail sooner than the basic formula predicts.

A useful derived metric is the maximum safe load: divide the allowable shear stress by the Wahl-corrected stress-per-unit-load to find the load at which the spring reaches its design limit. Music wire and chrome-silicon steel are the classic spring materials; their allowable stresses depend on wire diameter and whether the load is static or fatiguing, so always confirm against the wire supplier's table.

1. Choose the spring material to set the shear modulus and allowable stress.
2. Enter the wire diameter d and the mean coil diameter D (or compute D from outer diameter and wire).
3. Enter the number of active coils N.
4. Enter the applied load F, or solve for the load at a target deflection.
5. Click Calculate for spring rate, deflection, stress and Wahl factor.

Why is wire diameter raised to the fourth power?

The spring rate formula k = Gd⁴/8D³N comes from the torsion of the wire: the wire's polar moment of inertia scales as d⁴. This is why a small increase in wire thickness produces a huge increase in stiffness—a 10% thicker wire is about 46% stiffer.

What is the difference between active coils and total coils?

Active coils are the ones that actually flex when the spring is loaded. Compression springs are usually closed and ground at the ends, so the end coils sit flat and contribute little; subtract 2 from the total coils for a closed-end spring to get N.

What is a good spring index?

A spring index C = D/d between 4 and 12 is the design sweet spot. Below 4 the coils are too tight to wind reliably and the Wahl factor pushes stress up; above 12 the spring gets laterally unstable and tends to buckle under compression.

How do I know the allowable stress for my spring wire?

The wire supplier publishes allowable shear stress tables by wire diameter and load type. For music wire (ASTM A228) at 2 mm, static allowable shear is around 700–800 MPa, but for 10 million cycles it drops to roughly 350–400 MPa. Always use the fatigue value for cycled springs.

What is set removal and why is it done?

Manufacturers compress new springs to solid height a few times to remove the residual stress and take out the initial set. A spring that has not been set-removed will sag when first loaded, permanently lowering its free length and changing its rate.

Does the calculator handle extension or torsion springs?

The rate formula is the same for extension springs with active coils. Torsion springs use a different equation based on the wire's bending rather than torsion. This tool focuses on compression and extension springs with axial loading.

A spring index between 4 and 12 is the practical band—below 4 the wire is too thick relative to the coil and difficult to wind; above 12 the spring is floppy and buckles under load. Count active coils correctly: for a compression spring with closed ends, subtract 2 from the total coils. Springs under repeated load must be designed on the fatigue strength, not the static strength—the allowable stress drops sharply with more cycles. Always leave some free travel; a spring compressed to solid height takes a permanent set that changes its rate.