Fatigue Factor of Safety Calculator

The Goodman line joins Se on the alternating axis to Sut on the mean axis: σm = 100 and σa = 80 MPa with Se = 250 and Sut = 600 MPa give n = 2.05479.

Criterion:

GoodmanSoderbergGerber

Mean stress σm (MPa):

Alternating stress σa (MPa):

Endurance limit Se (MPa):

Corrected for size, surface and other factors.

Ultimate tensile strength Sut (MPa):

Yield strength Syt (MPa):

Factor of safety n (Goodman) =

2.05479452054794

Precision

Full answer, then cut to fewer decimals (not rounded):

2.05479452054794
2.0547945205479
2.054794520547
2.05479452054
2.0547945205
2.054794520
2.05479452
2.0547945
2.054794
2.05479
2.0547
2.054
2.05
2.0

Goodman: 2.05479
Soderberg: 1.84426
Gerber: 2.55731
First-cycle yield (Langer) Syt/(σa + σm): 2.5

Step-by-step solution

1/n = σa/Se + σm/Sut
σa/Se = 0.32, σm/Sut = 0.166667, σm/Syt = 0.222222
n = 2.05479

Fatigue Factor of Safety Formula

1/n = σa/Se + σm/Sut (Goodman)

Soderberg uses Syt; Gerber nσa/Se + (nσm/Sut)² = 1

Worked Example

σm = 100 MPa, σa = 80 MPa, Se = 250 MPa, Sut = 600 MPa, Syt = 450 MPa:

1/n = σa/Se + σm/Sut
σa/Se = 0.32, σm/Sut = 0.166667, σm/Syt = 0.222222
n = 2.05479

Soderberg: 1.84426 · Gerber: 2.55731 · First-cycle yield (Langer) Syt/(σa + σm): 2.5

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Frequently asked questions

Which fatigue criterion is most conservative?

Soderberg, because it uses the yield strength; Goodman is in between, and Gerber’s parabola is the least conservative.

How are mean and alternating stresses defined?

σm = (σmax + σmin)/2 and σa = (σmax − σmin)/2.

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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APA

Scientific Converters. (2026, October 15). Fatigue Factor of Safety Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/fatigue-factor-of-safety-calculator/

IEEE

Scientific Converters, "Fatigue Factor of Safety Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/fatigue-factor-of-safety-calculator/