Science & Engineering
Compression spring stress.
Shear stress in a round-wire helical compression spring, τ = Kw · 8FD ÷ (πd³), with the Wahl correction factor and spring index, the maximum load for an allowable stress and the solid length. Runs in your browser.
Spring and load
Result
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Worked example
The spring from the Spring Rate Calculator (2 mm wire, 16 mm mean coil diameter) compressed to 48.4 N: spring index C = 16 ÷ 2 = 8. Wahl factor Kw = (4 × 8 − 1) ÷ (4 × 8 − 4) + 0.615 ÷ 8 = 1.1840. Uncorrected stress 8FD ÷ πd³ = 246.5 MPa, so corrected shear stress is 291.9 MPa. With a 10-coil closed-and-ground spring the solid length is 10 × 2 = 20 mm. (If your wire maker allowed, say, 600 MPa, the maximum load would be 99.5 N.)
How it works
A helical compression spring is, in effect, a torsion bar wound into a coil, so the wire sees shear stress. The basic value is 8FD ÷ (πd³), where F is the load, D the mean coil diameter and d the wire diameter. Curvature of the coil and direct shear raise the stress on the inside of the coil, so it is multiplied by the Wahl factor Kw = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C, with spring index C = D ÷ d. Kw rises quickly as C falls (about 1.58 at C = 3 and 1.09 at C = 16); most helical springs have an index between 3 and 12.
The maximum load for an allowable stress is the same equation turned round, Fmax = τallow π d³ ÷ (8 Kw D). Solid length depends on the end type: d × (total coils + 1) for plain or closed ends that are not ground, and d × total coils for ground ends; the sources note these are not exact. This page does not supply allowable stresses, because they depend on the wire material, size and surface treatment; get them from the wire maker.
Not for safety-critical design
Planning and learning aid only. It is not for structural, lifting, pressure-system or other safety-critical design, and it is not professional engineering advice. Have a qualified engineer check anything that carries people or could fail dangerously.
Sources and basis: Roy Mech: Helical springs (Wahl factor, spring index, solid length); AMESWeb: Compression spring formulas (shear stress, Wahl factor, spring index). Checked 2026-10-16. Planning aid only; see the note above.
FAQ
What is the Wahl factor?
A correction Kw = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C that multiplies the basic spring shear stress to allow for coil curvature and direct shear. C is the spring index D ÷ d.
What is the shear stress formula for a compression spring?
τ = Kw × 8FD ÷ (πd³), where F is the load, D the mean coil diameter, d the wire diameter and Kw the Wahl factor.
What spring index is normal?
Most helical springs have an index D ÷ d between 3 and 12. Very low indexes are hard to wind and have a large Wahl factor; very high ones tend to tangle and buckle.
What allowable stress should I use?
It depends on the wire material, diameter, surface condition and whether the spring cycles. Take it from the wire maker's data; this calculator does not give one.
How is the solid length found?
For ground ends it is wire diameter times total coils; for plain or closed ends that are not ground it is wire diameter times total coils plus one. These are approximate.