Fatigue Life Calculator (Basquin)
Cycles and running hours to fatigue failure at a stress amplitude, with the stress giving a million cycles.
Results
What this tool does
Fatigue life falls steeply with stress: the exponent means a twenty percent stress reduction can multiply the life several times over. That is why fatigue problems are solved by removing stress concentrations rather than by using stronger steel — a sharp corner costs more life than a grade change buys back.
Formula
S = a N^b → N = (S ÷ a)^(1/b) (Basquin's relation)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sa | Stress amplitude | MPa |
ca | Fatigue strength coefficient | MPa |
bx | Fatigue strength exponent | — |
fq | Frequency | Hz |
NC | Cycles to failure | — |
HR | Hours | h |
YR | Years | — |
S6 | Stress amplitude | MPa |
DM | Damage per hour | — |
Worked example
- Stress amplitude250 MPa
- Fatigue strength coefficient1200 MPa
- Fatigue strength exponent-0.12
- Frequency5 Hz
- Cycles to failure475,347
- Hours26.41 h
- Years0.0030
- Stress amplitude228.655 MPa
- Damage per hour0.03786711
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Where do the coefficient and the exponent come from?
From fatigue testing of the specific material and, crucially, the specific detail: a polished specimen, a welded joint and a bolted connection made of the same steel have completely different curves. Design codes publish the constants for standard details, and materials handbooks publish them for test specimens. The defaults here are illustrative only — a fatigue assessment that matters has to use the constants from the applicable code, with the correction factors for surface, size and mean stress that this simple relation leaves out.