Helical Compression Spring Calculator
Spring rate, deflection under load, spring index, Wahl factor and the corrected shear stress.
Results
What this tool does
Rate goes with the fourth power of the wire diameter and inversely with the cube of the coil diameter, which is why a tenth of a millimetre on the wire changes everything and why springs are so sensitive to manufacturing tolerance. Shear modulus is about 79.3 GPa for music wire and carbon spring steel, around 69 GPa for stainless.
Formula
k = G d⁴ ÷ (8 D³ n) ; τ = K 8 F D ÷ (π d³)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
gm | Shear modulus | GPa |
dw | Wire diameter | mm |
dc | Mean coil diameter | mm |
na | Active coils | — |
fs | Force | N |
KS | Spring constant | N/mm |
DF | Deflection | mm |
CI | Spring index | — |
KW | Wahl factor | — |
TA | Stress | MPa |
EN | Energy | J |
Worked example
- Shear modulus79.3 GPa
- Wire diameter4 mm
- Mean coil diameter25 mm
- Active coils8
- Force100 N
- Spring constant20.3008 N/mm
- Deflection4.9259 mm
- Spring index6.2500
- Wahl factor1.24126
- Stress123.470 MPa
- Energy0.24630 J
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
What is the Wahl factor correcting for?
The simple torsion formula assumes the wire is straight, but in a spring it is curved, so the inside of the coil is stressed more than the outside. The Wahl factor adds that curvature effect plus the direct shear the simple formula ignores. It matters most in tightly wound springs: at a spring index of 4 it adds nearly forty percent, while at 12 it adds barely twelve. An index between 6 and 10 is the usual compromise between that stress concentration and the difficulty of coiling.