The Wahl correction factor

The simple torsional formula for shear stress in a helical spring, τ = 8·F·D/(π·d³), assumes the wire is a straight torsion bar. A spring wire is curved, and the coil curvature crowds the stress onto the inner surface of the coil — exactly where springs fail. The Wahl correction factor accounts for that curvature plus the direct (transverse) shear:

Kᵥᵥ = (4C − 1) / (4C − 4) + 0.615 / C, where C = D / d

Here C is the spring index — the ratio of mean coil diameter to wire diameter. The corrected peak shear stress is then:

τ = Kᵥᵥ · 8·F·D / (π·d³)

How big is the correction?

The factor is largest for tightly-wound springs (low index) and approaches 1 as the coil gets relatively large:

• Index C = 4 → Kᵥᵥ ≈ 1.40 (40% higher than uncorrected)
• Index C = 8 → Kᵥᵥ ≈ 1.18
• Index C = 10 → Kᵥᵥ ≈ 1.14
• Index C = 12 → Kᵥᵥ ≈ 1.12

Skipping the factor on a C = 4 spring under-predicts the real peak stress by 40% — enough to turn a “safe” design into one that yields or fatigues. That is why the correction matters most exactly where springs are most highly stressed.

Why the inner fibre

When a curved wire is twisted, the material on the inside of the curve sees a shorter moment arm and higher shear strain than the outside. The transverse shear from the applied load adds to it on the same inner fibre. The combined effect is a stress concentration on the coil’s inner diameter, which the Wahl factor captures in a single multiplier.

Wahl vs Bergsträsser

A common alternative is the Bergsträsser factor K_B = (C + 0.5)/(C − 0.75), which is simpler and agrees with Wahl’s to within about 1% across the practical index range. Some texts separate the pure curvature factor from the direct-shear factor. Any of these is acceptable engineering practice; this site uses the Wahl factor.

The calculator applies the Wahl factor automatically and compares the corrected stress against the material’s size-dependent allowable, so you see immediately whether a design has margin.

Frequently asked questions

What is the Wahl correction factor?

It is a multiplier that corrects the simple torsional shear stress in a helical spring for the extra stress on the inner coil surface caused by curvature and direct shear: Kᵥᵥ = (4C−1)/(4C−4) + 0.615/C, where C = D/d.

Do I always need the Wahl factor?

For any real spring, yes — the uncorrected formula under-predicts the peak stress, and the inner fibre is where springs actually fail. Only ignore it for a rough first estimate.

What is the difference between the Wahl and Bergsträsser factors?

Both correct the same effect. Bergsträsser’s K_B = (C+0.5)/(C−0.75) is simpler and within about 1% of Wahl’s for typical indices; Wahl’s separates curvature and direct-shear terms. Either is acceptable.

use the compression spring calculator.

Last reviewed: 2026-05-29.