What is an S-N curve?

An S-N curve (Wöhler curve) plots stress amplitude (S) versus number of cycles to failure (N) on a log-log scale. It characterizes a material's fatigue behavior and is used to predict fatigue life under cyclic loading.

What is the Basquin equation?

The Basquin equation σa = a·N^b (or equivalently N = (σa/a)^(1/b)) describes the S-N curve in the high-cycle fatigue regime. Constants 'a' and 'b' are determined from material testing. Typical b values range from -0.05 to -0.12.

What is the endurance limit?

The endurance limit (Se) is the stress amplitude below which a material can theoretically withstand infinite cycles without failure. Steel and titanium typically exhibit an endurance limit at ~10⁶-10⁷ cycles, roughly 40-50% of UTS. Aluminum and copper do not have a true endurance limit.

What factors affect fatigue life?

Surface finish, stress concentration (notches, holes), mean stress, temperature, environment (corrosion), loading type (bending vs axial vs torsion), residual stresses, and material microstructure all significantly affect fatigue life.

How accurate is the S-N approach?

The S-N approach is widely used for high-cycle fatigue (>10⁴ cycles) and provides reasonable estimates. However, scatter in fatigue data is large — life predictions typically have a factor of 2-3 uncertainty. For critical applications, use probabilistic approaches and testing.

Free Engineering Tool

Fatigue Life Calculator

Estimate cycles to failure using the S-N curve approach and Basquin equation. Enter stress amplitude, material constants, and endurance limit.

S-N CurveBasquin Equation#170

Results

Cycles to Failure N

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Basquin Exponent b

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Basquin Coefficient a (σ’f)

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Assessment

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S–N Curve (Wöhler Diagram)

Basquin Equation (High-Cycle Fatigue)

The constants a (fatigue strength coefficient) and b (fatigue strength exponent) are derived from two known points on the S-N curve: (N=1000, σ≈0.9·UTS) and (Ne, Se).

⚠️ Note: If σ_a ≤ Se, the component has infinite life (below endurance limit). This calculator uses the simplified Basquin approach and does not account for mean stress (Goodman/Gerber) or surface finish corrections.

Fatigue Life Calculator | S-N Curve | Basquin Equation | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Basquin Equation (High-Cycle Fatigue)