What is the Basquin equation?

The Basquin power law can be written σ_a = C · N^b for cycles N, with a negative exponent b. Rearranging gives N = (σ_a / C)^(1/b). Some strain-life conventions use reversals 2N instead; this calculator uses the cycles form stated here.

What are typical values for b?

For most metals b is negative, ranging from about -0.05 (high-cycle, hard metals) to -0.15 (low-cycle, ductile materials). Steel typically shows b ≈ -0.085, aluminum ≈ -0.10.

What is the fatigue strength coefficient C?

C (also called σ_f') is the intercept of the S-N curve at 1 cycle and is approximately equal to the true fracture strength. A common approximation is C ≈ 1.5 × UTS for steels.

Does this account for mean stress?

No. The Basquin equation assumes fully-reversed (zero mean stress) loading. For non-zero mean stress, apply a correction such as the Goodman or Morrow correction before entering σ_a.

What is the endurance limit?

Many ferrous materials exhibit an endurance limit — a stress below which fatigue life is theoretically infinite. The Basquin model itself does not include a hard cutoff; the calculator flags the 10^6 and 10^7 cycle benchmarks as practical references.

How accurate is this calculation?

The result is a first-order estimate. Real fatigue life is influenced by surface finish, stress concentrations, environment, and statistical scatter. Apply appropriate safety factors (typically 2–4 on cycles) in design.

Fatigue Life Calculator

Calculate the number of cycles to failure for a material under cyclic loading using the Basquin S-N relationship.

Material & Loading Inputs

Basquin power-law S-N model: N = (σₐ / C)^1/b

Stress Amplitude σₐ (MPa)

Half the peak-to-valley stress range. Must be > 0.

Fatigue Strength Coefficient C = σ′₀ (MPa)

S-N intercept at 1 cycle; ≈ 1.5 × UTS for steel.

Fatigue Strength Exponent b (dimensionless, negative)

Typically −0.05 to −0.15. Must be negative.

Quick Presets

Results will appear here

Enter stress amplitude and material constants, then click Calculate.

Cycles to Failure

cycles

10³ cycles 10⁶ cycles 10⁹ cycles

Position on a log scale from 10³ to 10⁹ cycles

Fatigue Regime

Applied Formula

Input Summary

Stress Sensitivity

Cycles to failure at different stress amplitudes with the same material constants.

σₐ (MPa)	N (cycles)	Regime

Summary

The Fatigue Life Calculator estimates how many stress cycles a material can endure before failure using the Basquin (power-law) S-N relationship: N = (σ_a / C)^(1/b), where σ_a is the stress amplitude, C is the fatigue strength coefficient, and b is the negative fatigue strength exponent. This approach models the classic Wohler S-N curve used in mechanical engineering and materials science. Results help engineers size components, predict service life, and select materials for cyclic loading applications.

How it works

Enter the stress amplitude (σ_a) applied to the material in MPa.
Enter the fatigue strength coefficient (C, also written σ_f') in MPa — often 1.5–2× the ultimate tensile strength.
Enter the fatigue strength exponent (b) — a negative dimensionless value, typically between -0.05 and -0.15 for metals.
The calculator applies the Basquin equation N = (σ_a / C)^(1/b) to compute cycles to failure.
The result is displayed in engineering notation alongside the safety margin relative to 10^6 and 10^7 cycle endurance benchmarks.

Use cases

Estimate service life of rotating shafts, gears, and fasteners under cyclic loading.
Compare fatigue performance of candidate materials at a given stress amplitude.
Verify that a design stress stays well below the endurance limit for infinite-life design.
Perform quick parametric studies on how changing stress amplitude affects component life.
Support failure analysis by back-calculating stress from known cycle count.
Teach students the Basquin power-law model and S-N curve concepts.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu