Spring Rate / Deflection Calculator
Calculate compression/extension spring rate, deflection, spring index, and shear stress
Results
Spring Rate k
—
Deflection δ
—
Spring Index C
—
Wahl Factor Kw
—
Max Shear Stress τ
—
Stress / Allowable
—
Stress Utilization
Formula Reference
Spring rate: k = G × d⁴ / (8 × D³ × Na)
Deflection: δ = F / k
Spring index: C = D / d
Wahl correction factor: Kw = (4C−1)/(4C−4) + 0.615/C
Max shear stress: τ = Kw × 8FD / (π × d³)
Allowable shear stress: τallow ≈ 0.45 × Sut (typical static yield)
Worked Example
| Parameter | Value |
|---|---|
| Wire diameter d | 0.125 in |
| Mean coil diameter D | 1.0 in |
| Active coils Na | 10 |
| Material | Music Wire G = 11.5 Mpsi |
| Load F | 50 lbf |
| Spring Rate k | 11.5e6 × 0.125⁴ / (8 × 1³ × 10) = 35.0 lbf/in |
| Deflection δ | 50 / 35.0 = 1.43 in |
| Spring Index C | 1.0 / 0.125 = 8 |
| Wahl Factor Kw | (4×8−1)/(4×8−4) + 0.615/8 = 1.184 |
| Shear Stress τ | ≈ 87,700 psi |