Extension spring calculator
Calculate the rate, initial tension and maximum load of extension springs with hooks. Enter the dimensions and the hook-to-hook length.
Formula
Symbols
Worked example
Computed by the same engine as the calculator above, using the form's starting values.
Extension springs work under pull load and carry an initial tension that must be overcome before the coils separate.
The tool estimates initial tension from geometry and validates that the hooks fit within the overall length.
Hooks are usually the weak point: bending stress at the loop limits the load before the spring body does. The full designer computes that limit for each hook style.
How to measure your spring
- Measure the wire diameter (d) on the body, not on the hook.
- Measure the outer diameter (OD) across the closed coils.
- Measure the hook-to-hook length (end to end, inside the hooks) with no load.
- Count the body coils. On extension springs every body coil is active.
- Identify the hook style: machine loop, crossover loop, side loop, extended hook or swivel eye.
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 is initial tension in an extension spring?
It is the force wound into the spring that holds the coils closed. The spring only starts to extend once the load exceeds that force, so F = IT + k·x.
How do I measure the rate of an extension spring?
Measure the force at two different lengths and divide the force difference by the travel difference. Using two points cancels initial tension out of the math.
Do hooks affect the strength of the spring?
Yes. The loop concentrates bending stress and typically fails before the body. Extended hooks and swivel eyes change both the usable length and the load limit.
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