Calculator · Structural Mechanics
Factor of Safety Calculator
The factor of safety compares a capacity with the demand currently placed on it. Both are compared as magnitudes, so the answer tells you how much larger the strength is than the working stress — not in which direction the stress acts.
Strength basis
The basis is a label on your own number — it records which capacity you compared against and does not change the calculation.
Inputs
A normal stress, a von Mises equivalent stress, or any measure consistent with S.
Results
| Yield strength | 250 MPa |
|---|---|
| Working stress σ | 150 MPa |
| Demand |σ| | 150 MPa |
| Factor of safety n = S/|σ| | 1.6667 |
| Utilisation |σ|/S | 60 % |
| Verdict | demand below the stated strength |
Assumptions
- · The factor of safety compares magnitudes: n = S / |σ|.
- · The reference strength and the working stress must be the same kind of stress measure, consistently defined.
- · A factor of safety is not a design-code check; the governing criterion depends on material, failure mode and standard.
Technical reference
n = S / |σ|
utilisation = |σ| / S
- S
- reference strength: yield, ultimate, or a declared allowable[Pa]
- σ
- working stress compared against that strength[Pa]
- n
- factor of safety, dimensionless[–]
The answer is only as meaningful as the pairing. A von Mises stress belongs against a yield strength; a peak normal stress in a brittle material belongs against an ultimate strength. Mixing bases silently changes what the number means.
At zero working stress the ratio has no finite value. That is reported as such rather than as an infinite factor.
This is not a code check. Design codes apply partial factors to loads and resistances separately and may require several limit states to be verified; a single global factor does not replace them.