Fatigue Safety Factor Calculator
The fatigue safety factor determines whether a component subjected to cyclic (fluctuating) loading will survive its design life without fatigue fracture. This calculator applies the Modified Goodman criterion, which relates the alternating stress amplitude and the mean stress to the material's corrected endurance limit and ultimate tensile strength. Enter the stress state, material properties, and optional endurance limit correction factors to determine the safety factor against fatigue failure.
Modified Goodman criterion
nf = 1 / [(sigmaa / Se) + (sigmam / Sut)]
ny = Sy / (sigmaa + sigmam)
n = min(nf, ny)
Where: sigma(a) = alternating stress amplitude (MPa), sigma(m) = mean stress (MPa), Se = corrected endurance limit (MPa), Sut = ultimate tensile strength (MPa), Sy = yield strength (MPa). The controlling safety factor is the lesser of fatigue failure n(f) and first-cycle yielding n(y).
Endurance limit corrections
- Surface factor ka: Ground surface 1.0; Machined/cold-drawn 0.80-0.95; Hot-rolled 0.65-0.80; As-forged 0.50-0.65.
- Size factor kb: d less than 8 mm: 1.0; 8-51 mm: 0.85-0.9; Greater than 51 mm: 0.70-0.85.
- Load factor kc: Bending 1.0; Axial 0.85; Torsion 0.59 (or use von Mises equivalent stress).
- Reliability factor ke: 50%: 1.0; 90%: 0.897; 95%: 0.868; 99%: 0.814; 99.9%: 0.753.
Fatigue safety factor calculator: frequently asked questions
What is the Modified Goodman criterion?
The Modified Goodman diagram is the most widely used method for fatigue analysis of ductile metals. It states that failure occurs when (sigma_a / Se) + (sigma_m / Sut) = 1, where sigma_a is the alternating stress amplitude, sigma_m is the mean stress, Se is the corrected endurance limit, and Sut is the ultimate tensile strength. The safety factor n = 1 / [(sigma_a / Se) + (sigma_m / Sut)].
What is the endurance limit?
The endurance limit Se is the maximum cyclic stress amplitude below which a material can theoretically endure an infinite number of cycles without fatigue failure. For steels with Sut less than 1,400 MPa, the test specimen endurance limit Se' is approximately 0.5 * Sut. The corrected endurance limit Se = ka * kb * kc * kd * ke * Se', where k factors account for surface finish, size, loading, temperature, and reliability.
What are the Marin modification factors?
The Marin factors correct the test specimen endurance limit for real component conditions: ka = surface finish factor (ground: 1.0, machined: 0.8-0.9, as-forged: 0.5-0.7); kb = size factor (0.9 for d less than 50 mm, lower for larger); kc = load type factor (1.0 for bending, 0.85 for axial, 0.59 for torsion); kd = temperature factor; ke = reliability factor (0.90 for 90%, 0.814 for 99%).
What safety factor is recommended for fatigue?
Typical design safety factors for fatigue range from 1.5 to 2.5 for well-understood loads and materials (Shigley's Mechanical Engineering Design), 2 to 4 for less certain loads, and above 4 for critical components where failure would be catastrophic. ASME pressure vessels use a fatigue safety factor of 3 on stress amplitude for low-cycle fatigue.
What is the difference between Goodman, Gerber, and Soderberg criteria?
Goodman (1899): linear relationship between sigma_a and sigma_m, uses Sut as the anchor. Conservative and widely used. Gerber (1874): parabolic relationship, less conservative than Goodman, better fits experimental data. Soderberg (1930): uses yield strength Sy instead of Sut, most conservative. Goodman is the standard for general engineering design.
Official sources
- ASTM E466 Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests: ASTM E466.
- NIST Materials Data Repository: materialsdata.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.