Factor of safety

Factor of safety (FoS, also called safety factor) is the ratio of the limit value at which a part would fail to the value it is actually subjected to in service. It is most often calculated from stresses: FoS = Sy / σ, where Sy is the yield strength of the material and σ is the highest equivalent (von Mises) stress in the part. A value of 2 means the part would begin to deform plastically at twice the load, provided it behaves linearly.

The factor is determined separately for each way the part can fail: against yield for ductile materials, against ultimate strength for brittle materials (cast iron, ceramics, some plastics), against the critical load for buckling and against the endurance limit for cyclic loading. The lowest value always governs. The required factor, chosen by the designer up front, defines the allowable stress (for example σallow = Sy / FoS); the actual factor is what the calculation delivers.

The choice depends on how well the loads, material and analysis model are known and on the consequences of failure. For ductile metals under well-known static loads, 1.5 to 2 is typical; with uncertain loads or impacts, 2 to 3; for brittle materials and buckling, higher still. Aerospace applies a factor of 1.5 to the limit load, the largest load expected in service, balanced by precise analysis, testing and material control.

For lifting equipment, pressure vessels and building structures, the applicable standards and regulations prescribe the values or the procedure. Instead of a single overall factor, the Eurocodes for structures (like load and resistance factor design, LRFD, in the US) use partial factors, separate for loads and for materials.

The factor of safety is the main output of every structural analysis and the basic criterion for whether a design passes. Set the required value early, in the product requirements specification, so the calculation and the tests have a clear acceptance criterion. When lightweighting a design, it shows where there is more material than needed and where the margin falls short.

For plastic and 3D-printed parts, higher values than for metals are usually chosen because of property scatter, anisotropy, temperature effects and creep, or reduced long-term material values are used in the calculation.

A high factor of safety does not guarantee a safe part. If a load case is missing, the analysis ignores material fatigue or the stress concentration at a notch, or the material does not match the assumption, even a factor of 5 can be misleading. Conversely, an unnecessarily high factor "just to be safe" leads to heavy, expensive parts. Also beware of stacked margins: if the load already includes an impact allowance and the analysis uses conservative assumptions, another high factor only adds weight.

Always state what the factor refers to (yield, ultimate strength, buckling, fatigue), which load case it applies to and whether the loads are service loads or already factored up. Without that, two values cannot be compared. With linear FEA, watch out for local stress peaks at singularities, which make the factor look lower than it is, and for regions above yield, which a linear analysis does not describe correctly.