Spring Rate Calculator
Calculate the rate, force and stress of a helical compression spring.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Spring Rate Calculator does
A helical compression spring works by twisting its wire. Its stiffness therefore depends on the shear modulus and, very strongly, on wire diameter — to the fourth power — while more coils and a larger coil diameter both make it softer.
Formula
k = G d⁴ ÷ (8 D³ n)Spring index C = D ÷ dWahl factor K = (4C − 1)/(4C − 4) + 0.615/CShear stress τ = K × 8 F D ÷ (π d³)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Spring material | one of 5 options | Yes | — |
| Wire diameter | number | Yes | — |
| Wire diameter unit | one of 9 options | Yes | — |
| Mean coil diameter | number | Yes | Measured centre to centre of the wire. |
| Mean coil diameter unit | one of 9 options | Yes | — |
| Active coils | number | Yes | Accepts 0.5 or more. |
| Deflection | number | Optional | — |
| Deflection unit | one of 9 options | Yes | — |
| Custom shear modulus | GPa | Optional | Accepts 0 or more. |
How to use it
- Choose Spring material and Wire diameter unit.
- Enter Wire diameter, Mean coil diameter and Active coils.
- Optionally add Deflection and Custom shear modulus.
- Select Calculate.
Worked example
A music wire spring, 2 mm wire, 20 mm mean coil diameter, 10 active coils.
- Material
- Music wire
- Wire
- 2 mm
- Coil
- 20 mm
- Coils
- 10
k = 81.7 GPa × 0.002⁴ ÷ (8 × 0.02³ × 10) = 2,042 N/m, or 2.04 N/mm. Spring index is 10 — at the upper end but workable.
Frequently asked questions
Why does wire diameter matter so much?
Rate goes with the fourth power of wire diameter. Increasing wire from 2.0 to 2.2 mm raises stiffness by 46% with everything else unchanged.
What is a good spring index?
Between 4 and 12, ideally 5 to 9. Tighter indices are hard to coil and highly stressed; looser ones buckle and tangle.
Method and sources
Method. Helical compression spring rate, k = Gd⁴ ÷ (8D³n), from wire diameter, mean coil diameter, active coils and shear modulus.
Assumptions
- A helical spring of constant pitch and diameter operating within its elastic range, with the stated number of active coils.
Limitations
- Rate is acutely sensitive to wire diameter, which appears to the fourth power: a 2% manufacturing variation moves the rate by roughly 8%.
- Counting active coils is the usual source of error, since end coils contribute partially depending on how they are ground and closed.
- The linear rate holds until coils begin to touch; approaching solid height, the spring stiffens sharply and the formula no longer applies.
Sources
- Standard helical spring design relationships — Established machine design references; material shear modulus from the wire specification. The rate formula and the role of each geometric term.