Factor of Safety Calculator

What is a factor of safety?

The factor of safety is the ratio of the limiting value a member can take to the value it sees in service: n = strength / load effect. A part with a yield strength of 250 MPa working at 100 MPa has a factor of 2.5. A value of 1 means the part is at its limit and anything below 1 means the limit is exceeded.

The same ratio is written for loads. A member with a breaking load of 60 kN carrying 12 kN has a factor of 5.

Allowable stress

The reverse use is just as common. When a standard prescribes a factor, allowable stress = strength / n, and the working stress is kept below it. For a yield strength of 355 MPa and a factor of 1.5 the allowable stress is 236.7 MPa. This is the allowable stress design approach.

Margin of safety

Some fields quote a margin instead of a factor: margin of safety = n − 1. A factor of 2.5 gives a margin of 1.5, or 150 percent. A zero margin means the part is exactly at its limit.

Partial factors

Current structural codes use two separate factors instead of one. The load is increased by a load factor: E_d = γ_F × E_k. The resistance is reduced by a material factor: R_d = R_k / γ_M. The condition is E_d ≤ R_d. With a characteristic load of 100 kN, a load factor of 1.5, a characteristic resistance of 200 kN and a material factor of 1.15, the design load effect is 150 kN and the design resistance 173.9 kN, so the check passes.

Limits

The factor itself is easy to calculate. The hard part is getting the strength and the load effect right. Stress concentration, fatigue, buckling, corrosion and load uncertainty change the answer substantially. The adequate factor depends on the application and is written in the relevant standard. This tool gives the ratio only, the choice of factor is yours.