Compression coil spring
Spring rate and load, torsional stress with the Wahl correction. Spring index and solid length checked too.
From the wire diameter, mean coil diameter and number of active coils, the tool gives the spring rate, then the load and torsional stress at the deflection you specify. The stress includes the Wahl stress correction factor.
At the same time it checks whether the spring index c falls in a sound range (4 to 15), and whether the compressed length has dropped below the solid length. Combinations that do not work as a design are flagged as you type.
| Spring index c = D/d | – |
|---|---|
| Wahl correction factor κ | – |
| Shear modulus G | –GPa |
| Allowable torsional stress τa (guide) | –MPa |
| Stress utilisation | –% |
| Solid length (Nt = Na+2) | –mm |
| Formulae used | k = G·d⁴/(8·D³·Na) τ = κ·8·D·P/(π·d³) |
What does the spring index c represent?
c = D/d, the mean coil diameter divided by the wire diameter. It is a dimensionless measure of how slender the spring is, and on its own it decides both manufacturability and stress.
A small c (thick wire wound tightly) makes the wire hard to deform plastically during coiling, so it is difficult to make. The curvature on the inside of the coil also becomes sharp, so the stress there rises above the outside and the concentration can no longer be ignored. Too large a c makes the spring long and thin, and it may buckle under compression or tangle with its neighbours.
In practice, keep it between 4 and 15, and aim for 6 to 10. This tool warns you when you leave that range. While the design is still open, fixing c before the load or the free length makes everything afterwards easier.
What is the Wahl correction factor?
The wire of a coil spring carries, on top of the torsion from the load, two effects that come from the coil shape: direct shear, and stress concentration from the curvature on the inside of the coil. The plain torsion formula τ = 8DP/(πd³) includes neither, so it returns a value below the truth.
The Wahl factor κ = (4c−1)/(4c−4) + 0.615/c corrects for both at once. At c = 6, κ ≈ 1.25 — that is, without the correction you underestimate the stress by more than 20 per cent. The smaller c is, the larger the correction.
This tool always shows the value with κ included. When comparing against another calculation, check whether the other one has the correction in it.
Solid length and free length
Solid length is the length when the coils are fully closed and the wire is touching itself. With Nt as the total number of coils, Lc ≈ Nt × d, and taking one closed coil at each end gives Nt = Na + 2.
If the maximum compression in use reaches solid length, the spring stops working as a spring. The load rises abruptly and damages both the wire and whatever the spring bears on. It is usual to leave 15 to 20 per cent of margin before solid. This tool warns you when the compressed length falls below solid length.
Note that this covers static loading. For cyclic use, check set (permanent deformation) and fatigue strength separately. The allowable torsional stress is a guide value on the assumption of static load.
This is a simplified calculation intended for first-pass sizing. Stress concentration, buckling, fatigue, welds, dynamic loading and temperature effects are not included. Yield, proof and allowable stress figures are representative guide values and are not guaranteed to match the standards themselves. Always carry out your own verification before building and manufacturing real hardware. We accept no liability for loss arising from the results of this tool.
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