# Factor of Safety

on . Posted in Dimensionless Numbers

Factor of safety, abbreviated as FS, also called safety factor, a dimensionless number, is the ability of a system's structural capacity to be usable beyond it's expected or acrual loads.  In other words a concept used in engineering and risk assessment to measure the safety margin or level of protection against failure or undesirable outcomes.  It is a ratio that compares the capacity or strength of a system or structure to the expected or design loads or forces acting upon it.

The factor of safety provides a measure of how much stronger or more capable a system is relative to the expected loads or forces.  A factor of safety greater than 1 indicates that the capacity is greater than the demand, suggesting a higher level of safety and a larger margin of strength.  A factor of safety less than 1 implies that the system is expected to fail or be compromised under the applied loads or forces.

The specific value of the factor of safety varies depending on the type of system or structure, its function, and the level of risk tolerance.  Factors of safety are typically chosen based on engineering standards, codes, and guidelines specific to the application or industry.  They are used to ensure the reliability, durability, and safety of structures and systems, ranging from buildings, bridges, and dams to mechanical components and equipment.  It's important to note that factors of safety are conservative design measures, aiming to mitigate uncertainties, variations in materials and construction, and unexpected conditions that can affect the performance and behavior of the system.

## factor of safety formula

$$\large{ FS = \frac {UTS}{R} }$$     (Factor of Safety)

$$\large{ UTS = FS \; R }$$

$$\large{ R = \frac{UTS}{FS} }$$

### Solve for FS

 ultimate tensile stress, UTS applied stress, R

### Solve for UTS

 factor of safety, FS applied stress, R

### Solve for R

 ultimate tensile stress, UTS factor of safety, FS

Symbol English Metric
$$\large{ FS }$$ = factor of safety $$\large{ dimensionless }$$
$$\large{ UTS }$$ = ultimate tensile stress $$\large{ \frac{lbf}{in^2} }$$ $$\large{ Pa }$$
$$\large{ R }$$ = applied stress $$\large{ \frac{lbf}{in^2} }$$ $$\large{ Pa }$$