Factor of Safety⚠ unverified
Physics / Materials · Factor of safety from ultimate strength and allowable stress
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| ultimate_strength | σult | Pa | 400000000.0 | Ultimate strength |
| allowable_stress | σallow | Pa | 100000000.0 | Allowable (working) stress |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| n | n | — | Factor of safety |
The science & history
Understanding the Parameters
-
$\sigma_{\mathrm{ult}}$ — often $S_{ut}$ from a tensile test; some codes use yield $S_y$ instead (then $n = S_y/\sigma_{\mathrm{allow}}$).
-
$\sigma_{\mathrm{allow}}$ — working stress used in sizing (may already include other factors).
- $n$ — e.g. 4 means ultimate is four times the allowable. Codes may prescribe minimum $n$.
Derivation (Approaching a Proof)
By definition of allowable stress design: choose $\sigma_{\mathrm{allow}} = \sigma_{\mathrm{fail}}/n$ so $n = \sigma_{\mathrm{fail}}/\sigma_{\mathrm{allow}}$. The calculator evaluates that ratio for the two stresses you supply.
History
Factors of safety are as old as engineered structures; modern LRFD/partial factors refine the idea with separate load and resistance factors.
Related Concepts: Von Mises Stress, Hooke's Law strain, Fatigue Endurance Limit, Euler Buckling Load
Notes: Registry calculator factor-of-safety (unverified). Definitional; failure metric is whatever
you put in $\sigma_{\mathrm{ult}}$.