What is the Basquin equation?

The Basquin (power-law) equation models the S-N curve as σ_a = C · (2N)^b, where σ_a is stress amplitude, N is cycles to failure, C is the fatigue strength coefficient (σ_f'), and b is the fatigue strength exponent. Rearranged for N: N = (C / σ_a)^(1/b) / 2, or in the single-amplitude form used here: N = (C / σ_a)^(1/b).

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

Name: Fatigue Life Calculator
Availability: InStock
Author: Nham Vu

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 = (C / σₐ)^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

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

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 = (C / σ_a)^(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

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