How to use this calculator
Enter the maximum and minimum stress in each load cycle (with any stress concentration factor already applied), the ultimate and yield strengths, and the corrected endurance limit Se. Pick a mean-stress criterion; modified Goodman is the usual choice in machine design courses.
Formulas
Worked example
1045 cold-drawn steel cycling from 40 to 200 MPa (the default)
- σa = (200 − 40)/2 = 80 MPa; σm = (200 + 40)/2 = 120 MPa.
- Goodman: 1/nf = 80/190 + 120/625 = 0.613, so nf = 1.63.
- Langer: ny = 530 / 200 = 2.65.
- Fatigue governs, with a safety factor of 1.63 for infinite life.
Assumptions and limits
- Infinite life (about 10⁶ cycles or more) for steels with an endurance limit.
- Se already includes Marin factors for surface, size, loading, temperature and reliability.
- Uniaxial stress. For combined stresses, use von Mises equivalent alternating and mean stresses.
- Compressive mean stress is conservatively ignored (nf = Se/σa).
Frequently asked questions
Which criterion should I use?
Modified Goodman is standard and slightly conservative. Gerber fits test data for ductile steels best. Soderberg is the most conservative and is rarely used today.
How do I get the endurance limit Se?
For steel, start with Se′ ≈ 0.5 Sut (up to 1400 MPa), then multiply by the Marin factors: Se = kakbkckdke Se′.
Do aluminum alloys have an endurance limit?
No. Aluminum keeps weakening with more cycles, so designers use the fatigue strength at a stated life, often 5 × 10⁸ cycles, in place of Se.
For education and preliminary checks only. Have a qualified engineer verify any design before it is built.