Factor of Safety: Definition, Equation, Examples, Calculator (With PDF)

The factor of safety or safety factor is a very important term in engineering design. While designing any Engineering product or component, safety is of utmost importance. To ensure the safety of those items, each component is designed to bear more loads than its actual operating loads. So, there will always be some margin or cushion as compared to its operating capabilities. This is ensured during the design stage by considering a suitable factor of safety. The factor of safety is defined as the ratio of ultimate stress of the component material to the working stress. It denotes the additional strength of the component than the required strength.

Importance of Factor of Safety

A factor of safety is related to the safety of people. It reduces the risk of failure of a component by adding some cushion in design. Also, there always will be some hidden circumstances or unknown parameters that can not be considered accurate in design. At the same time, the reliability of material is not 100% and the load used in design calculation is not the maximum load. So the factor of safety or safety factor provides protection against those unknown events to some extent.
Although all components are designed with a factor of safety, it’s always suggested to use those components within their design limit.

Factors Affecting Determination of Factor of safety

Component design codes & standards normally provide a minimum factor of safety for that component. However, choosing the exact safety factor is dependent on various parameters like

  • Material type Ductile vs Brittle
  • Loading type Static vs dynamic
  • Whether cyclical loads
  • The intensity of stress concentration
  • Unforeseen Misuse of the component
  • Accuracy and stress complexity during a calculation
  • Environment and design temperature and pressure.
  • Impact of failure
  • Cost of component or material
  • Corrosion rate
  • Maintenance frequency

Factor of safety equation

As defined in the first paragraph that the factor of safety is a ratio of two loads or two stresses. Mathematically factor of safety can be expressed as

Factor of safety=Ultimate Load (Strength)/Allowable Load (Stress)

As understood from the above equation the allowable stress is always less than the ultimate failure stress. Hence, the factor of safety is always greater than 1. The ultimate stress for brittle material is considered as ultimate tensile strength and for ductile material is considered as yield strength.

Also, as the equation for factor of safety is the ratio of two stress or load values, it is dimensionless. The difference between the Factor of Safety and 1 is known as Margin of safety. So,

Margin of safety= (Factor of safety-1).

Examples of Factor of Safety

Typical examples of the factor of safety for a few materials depending on application and loading types are listed below in table 1. However, please note that the table only provides a typical range or typical values to provide an example. Actual values for the factor of safety must be taken from the design standard of the relevant component. For example, the factor of safety for pressure vessel design must be taken from the ASME Sec VIII code.

Sr NoMemberTypical Factor of safety range
1Structural Members in building services2
2Pressure Vessel3.5 to 4
3Automobiles3
4Aircraft and Spacecraft1.2 to 3.0
5Aircraft components1.5 to 2.5
6Boilers3.5 to 6
7Bolts8.5
8Cast-iron wheels20
9Engine components6.0 to 8.0
10Heavy duty shafting10.0 to 12.0
11Lifting equipment – hooks ..8.0 to 9.0
12Pressure vessels3.5 – 6
13Turbine components – static6.0 to 8.0
14Turbine components – rotating2.0 to 3.0
15Spring, large heavy-duty4.5
16Structural steel work in buildings4.0 to 6.0
17Structural steel work in bridges5.0 to 7.0
18Wire ropes8.0 to 9.0
19Highly reliable materials where loading and environmental conditions are not severe1.3 to 1.5
20Moderately reliable materials where loading and environmental conditions are not severe1.5 to 2
21Ordinary materials where loading and environmental conditions are not severe2 to 2.5
22For use with less tried and for brittle materials where loading and average environmental2.5 to 3
23For use with materials where properties are not reliable and where loading and environmental conditions are not severe, or where reliable materials are used under difficult and environmental conditions3.0 to 4.0
24Impact Forces3.0 to 6.0
25Brittle Material1.0 to 6.0
Table 1: Typical Factor of Safety Range

Factor of safety calculator

Various factor of safety calculators is available online to calculate the values of the factor of safety with known ultimate strength and allowable stress values. Let’s take an example to calculate factor of safety for the following situation:

The yield strength of a ductile material is 240 MPa. If the material is subjected to a loading condition that generates the maximum allowable stress of 140 MPa. Then the factor of safety of that material is 240/140=1.7. However, note that both stress values are in the consistent unit before calculating the factor of safety.

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Anup Kumar Dey

I am a Mechanical Engineer turned into a Piping Engineer. Currently, I work in a reputed MNC as a Senior Piping Stress Engineer. I am very much passionate about blogging and always tried to do unique things. This website is my first venture into the world of blogging with the aim of connecting with other piping engineers around the world.

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