Factor of safety formula
The factor of safety is how much stronger a part is than it strictly needs to be. It is the ratio of the material strength to the actual working stress, and it absorbs the uncertainties in loads, materials, and analysis.
Variables
| FoS | Factor of safety | dimensionless |
| σlimit | Material strength (yield or ultimate) | psi or Pa |
| σactual | Actual working stress | psi or Pa |
Rearranged
σlimit = FoS × σactual
Worked example
A part made from steel with a 250 MPa yield strength carries a working stress of 100 MPa.
Divide strength by working stress: 250 / 100 = 2.5.
A factor of safety above one means the part is stronger than its load demands; the margin covers overloads, material variation, and imperfect analysis. Ductile parts are usually based on yield strength, brittle parts on ultimate. Typical values run from about 1.5 for well-known loads to 4 or more where consequences are severe.
Need the strength values to start from?
See the Yield Strength Chart and Ultimate Tensile Strength Chart.
Choosing a factor of safety
The right factor depends on how well the loads and material are known and on the cost of failure. Familiar, steady loads on a well-characterized ductile metal might use 1.5 to 2. Uncertain or shock loads, brittle materials, or risk to life push the factor to 3, 4, or higher. Codes often fix the value for a given application.
Yield or ultimate strength
For ductile materials the factor is usually taken on yield strength, because permanent deformation is the practical failure. For brittle materials, which break without yielding, it is taken on ultimate strength. Quoting a factor of safety without saying which strength it references is ambiguous.
FAQ
What is a factor of safety?
The ratio of a material strength to the actual working stress, showing how much margin a part has against failure.
What is a good factor of safety?
It depends on the application: around 1.5 to 2 for well-understood loads, and 3 to 4 or more where loads are uncertain or failure is dangerous.
Is factor of safety based on yield or ultimate strength?
Usually yield for ductile materials, since permanent deformation is the limit, and ultimate for brittle materials, which fail by fracture.