Factor of Safety
Ratio of ultimate strength to allowable stress.
Formula
Variables
Example
A part failing at 800 MPa but used to 200 MPa has a safety factor of 4.
How it works
The factor of safety compares the maximum stress a material can withstand before failure to the lower stress it is actually allowed to carry in service. It works because engineers deliberately design structures so the working stress stays well below the ultimate strength, giving a margin for uncertainty, defects, overloads, wear, and variations in material properties. A larger value means a greater margin between normal use and failure.
When to use it
Use this formula when checking whether a beam, bolt, shaft, cable, pressure vessel, or other structural part has enough strength for its intended load. It is especially useful in design and safety verification when you know both the material's ultimate strength and the allowable working stress.
Worked example, step by step
A steel bracket has an ultimate strength of 360 MPa and an allowable working stress of 120 MPa. FoS = σ_ult / σ_allow FoS = 360 / 120 FoS = 3 Final answer: the factor of safety is 3, meaning the bracket's ultimate strength is three times its allowable working stress.
Common mistakes to avoid
- Using yield strength instead of ultimate strength without checking which definition is required
- Mixing units, such as MPa and kPa, without converting them first
- Reversing the ratio and calculating allowable stress divided by ultimate strength
Did You Know?
Elevators are typically built with a safety factor of around 11 — their cables could hold far more than a full car.
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