Fatigue Life (S-N) Calculator
Fatigue failure occurs when a material is subjected to repeated cyclic loading at stress levels below the static yield strength. The S-N (stress-life) approach uses the Basquin power-law model to relate cyclic stress amplitude to cycles to failure. This is the most widely used method for high-cycle fatigue design in metals. Enter the stress amplitude (MPa), the fatigue strength coefficient (sigma_f', in MPa), and the fatigue strength exponent (b, a negative number typically between -0.05 and -0.12). For typical quenched and tempered steel (sigma_f' = 1,000 MPa, b = -0.09) at 400 MPa stress amplitude, the calculator estimates approximately 130,000 cycles to failure.
Basquin S-N formula
sigma_a = sigma_f' * (2N)^b
Solved for N: N = 0.5 * (sigma_a / sigma_f')^(1/b)
Where sigma_a is the stress amplitude (MPa), sigma_f' is the fatigue strength coefficient (MPa), N is cycles to failure, and b is the fatigue strength exponent (negative value). The factor of 2 converts cycles to reversals.
Interpreting S-N results
Fatigue life predictions using the Basquin model are statistical estimates, not exact values. Actual fatigue life can vary by an order of magnitude from specimen to specimen due to surface condition, residual stress, inclusions, and environmental effects. Safety factors of 2 to 4 on stress or 10 to 100 on cycles are typical in design. For critical structures, full statistical analysis per ASTM E739 (statistical analysis of linear or linearized S-N fatigue data) is recommended.
Fatigue life S-N: frequently asked questions
What is an S-N curve?
An S-N (stress vs. number of cycles) curve, also called a Wohler curve, plots the cyclic stress amplitude a material can withstand against the number of cycles to failure. It is the primary tool for high-cycle fatigue design and is characterized experimentally per ASTM E466.
What is the Basquin equation?
The Basquin equation is sigma_a = sigma_f' * (2N)^b, where sigma_a is stress amplitude, sigma_f' is the fatigue strength coefficient, N is cycles to failure, and b is the fatigue strength exponent (typically -0.05 to -0.12 for metals). Rearranged: N = 0.5 * (sigma_a / sigma_f')^(1/b).
What does the fatigue endurance limit mean?
Many steels exhibit a stress amplitude below which fatigue failure does not occur regardless of cycle count. This is the endurance limit (Se), typically about 40 to 50 percent of ultimate tensile strength. Non-ferrous metals and polymers generally do not have a true endurance limit.
What inputs are needed to use the S-N calculator?
You need the cyclic stress amplitude (half the peak-to-peak stress range), the fatigue strength coefficient (sigma_f'), and the fatigue strength exponent b. These are determined by curve-fitting to experimental fatigue data or from standard materials databases.
How does mean stress affect fatigue life?
A compressive mean stress extends fatigue life while a tensile mean stress reduces it. The Goodman or Morrow mean stress correction is applied on top of the S-N approach. This calculator uses the fully reversed (zero mean stress) Basquin model; apply a correction factor separately if mean stress is present.
Official sources
- ASTM E466, "Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests": astm.org.
- ASTM E739, "Statistical Analysis of Linear or Linearized Stress-Life (S-N) Fatigue Data": astm.org.
- ASM International, "ASM Handbook Vol. 19: Fatigue and Fracture": asminternational.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.