Engineering Reference

Spring Rate Calculator

Rate and force for a compression spring from its dimensions and material, using the standard spring rate formula.

Page last changed 2026-10-19 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

Spring rate is k = G·d⁴ ÷ (8·D³·N) — wire diameter to the fourth power over coil diameter cubed. That asymmetry is why small changes in wire diameter change the rate dramatically while changes in coil diameter have a much gentler effect.

Compression Spring Rate

The Formulas Used

Spring rate: k = G·d⁴ ÷ (8·D³·N)
Spring index: C = D ÷ d   Wahl factor: Kw = (4C − 1)/(4C − 4) + 0.615/C
Stress: τ = 8·F·D ÷ (π·d³) × Kw

The Spring Index Is the Design Constraint

The spring index C = D/d is the ratio of coil diameter to wire diameter, and it governs whether a spring is practically manufacturable. Below about 4 the coils are so tight that the spring is difficult to wind and the stress concentration is severe. Above about 12 the spring is floppy and prone to buckling. The practical range is 4 to 12, with 6 to 10 being the comfortable middle.

The Wahl factor in the outputs corrects for two effects the simple stress formula ignores: the direct shear across the wire, and the stress concentration on the inside of the coil, where the radius of curvature is smallest. It is the inside of the coil that fails, and the Wahl factor can raise the computed stress by 15% or more at low spring indices.

Frequently Asked Questions

How do I calculate spring rate?
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. For steel, G is about 11,500,000 psi.
What is the spring index and why does it matter?
It is the ratio of mean coil diameter to wire diameter, D/d. Practical springs fall between 4 and 12. Below 4 the spring is hard to wind and stresses concentrate; above 12 it is floppy and may buckle. Six to ten is the comfortable range.
Why does wire diameter matter so much?
Because it appears to the fourth power in the numerator, while coil diameter appears cubed in the denominator. Increasing the wire diameter by 10% raises the rate by about 46%, while increasing the coil diameter by 10% lowers it by about 25%.
How many coils are active?
Active coils are the coils free to deflect. For a spring with closed and ground ends, the two end coils are inactive, so a spring with 10 total coils has 8 active. Using total coils instead of active coils overestimates the spring's stiffness.
What is solid height and why does it matter?
The height of the spring when all coils touch, approximately wire diameter times (active coils + 2). A spring cannot be compressed past solid height, so the available travel is the free length minus solid height — a limit that catches people out when specifying a spring for a short stroke.

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