Spring constant calculator
Find the spring constant (spring rate) in lbf/in and N/mm of a helical spring from wire diameter, mean diameter and number of active coils.
Formula
Symbols
Worked example
Computed by the same engine as the calculator above, using the form's starting values.
The spring constant k = G·d⁴ / (8·D³·Na) is dominated by wire diameter (to the fourth power). Tune the parameters and watch the effect in real time.
Calculations use each catalog material's real shear modulus, listed in the table below.
For extension springs the same formula applies to the body, adding initial tension. For torsion springs the constant is angular and uses the elastic modulus instead.
Quick tuning: more or less force
- Thicker wire
- Smaller outer diameter
- Fewer active coils
- Thinner wire
- Larger outer diameter
- More active coils
How to measure your spring
- Measure the wire diameter (d) with calipers or a micrometer, away from the ends.
- Measure the outer diameter (OD) across the coils. The mean diameter is OD minus d.
- Measure the free length (FL) with no load, end to end.
- Count the total number of coils. Closed and ground ends reduce the active coil count.
- Identify the end type: closed and ground, closed, double closed or open.
Material moduli and density
| Material | Shear modulus G | Elastic modulus E | Density |
|---|---|---|---|
| Carbon steel (MW) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Stainless 302 (SS302) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.90 g/cm³ |
| Stainless 17-7 (SS177) | 11.0 × 10⁶ psi (75.8 GPa) | 29.4 × 10⁶ psi (203.0 GPa) | 7.81 g/cm³ |
| Stainless 316 (SS316) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.98 g/cm³ |
| Oil tempered MB (OT) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Chrome silicon (CS) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Hard drawn (HD) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Phosphor bronze (PB) | 6.0 × 10⁶ psi (41.4 GPa) | 14.9 × 10⁶ psi (103.0 GPa) | 8.86 g/cm³ |
| Beryllium copper (BC) | 7.0 × 10⁶ psi (48.3 GPa) | 18.6 × 10⁶ psi (128.0 GPa) | 8.25 g/cm³ |
| Chrome vanadium (CV) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
Frequently asked questions
What are the units of a spring constant?
lbf/in in imperial and N/mm in metric. The conversion is 1 N/mm = 5.710 lbf/in. Physics texts often use N/m: 1 N/mm = 1000 N/m.
Does the spring constant change with load?
Not on conventional helical springs: force versus deflection is linear until the coils touch. Conical and variable-pitch springs are progressive, with a rate that rises as coils bottom out.
Which parameter affects the spring constant the most?
Wire diameter, because it enters the formula to the fourth power. Doubling the wire multiplies the constant by 16. Mean diameter enters cubed in the denominator, so larger springs are softer.
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