Spring rate calculator
A music-wire spring of 2 mm wire, 20 mm outside diameter and 8 active coils has a rate of 3.40 N/mm (k = G·d⁴ / 8D³Na); with ground ends and a 60 mm free length it goes solid at 20.0 mm and carries 51 N at 45 mm. Enter the wire, the outside diameter, the coils, the ends and the free length for the rate, the solid height and pitch, the load at a working length and the shear stress, in millimetres or inches.
The spring is drawn to scale between its plates and compresses to the working length.
- Rate k
- Solid height Ls
- Total coils Nt
- Pitch p
- Load at 45.00 mm
- Shear stress there
- Load to solid
- Shear stress at solid
- Index C = D/d, Wahl KW
- 9.00, 1.162
- Buckles from L0 (flat plates)
How it’s calculated
with D = OD − d the mean coil Ø and K_W = (4C − 1)/(4C − 4) + 0.615/C, C = D/d. Ends: plain Nt = Na, L₀ = p·Na + d, Ls = d(Nt + 1); squared Nt = Na + 2, L₀ = p·Na + 3d, Ls = d(Nt + 1); squared and ground Nt = Na + 2, L₀ = p·Na + 2d, Ls = d·Nt. An extension spring’s loops add G/E to its active coils; F = Fi + k·y. In N/mm.
| Wire | G (GPa) | E (GPa) | k for this spring (N/mm) |
|---|---|---|---|
| Music wire, oil-tempered, chrome silicon | 79.29 | 206.8 | 3.399 |
| Stainless 302 / 304 | 68.95 | 193.1 | 2.956 |
Why does the solid height matter?
A compression spring that is pushed solid takes its highest stress and can set (lose free length) if the wire is overstressed there. Keep the working length clear of the solid height, and check the stress at solid against the wire maker’s limit for its size. Ground ends sit square and stand shortest when solid; plain ends are cheapest but sit badly. A long spring between flat plates can buckle sideways once its free length passes about 5.26 times its mean diameter: guide it on a rod or in a bore.