Factor of Safety Calculator
Find out whether a part has enough margin. Enter an applied stress (or build it from force and area), pick a material, and get the factor of safety against both yield and ultimate strength, the allowable stress at your target, the margin of safety, and a clear pass or fail, with a stress-concentration factor and derating built in.
Need the bending stress first? Get it from M, c, and I with the Stress Calculator, then bring the result here.
Combined loading uses the von Mises equivalent stress: sqrt(normal^2 + 3 x shear^2), compared to yield.
Material and limits
What is a factor of safety?
The factor of safety (FoS, sometimes called the safety factor) is how many times stronger a part is than it strictly needs to be for the load it carries. It is simply the material strength divided by the actual stress in the part: a factor of 2 means the part could take twice the stress before it reaches the strength limit. A factor below 1 means the part is overloaded and is expected to fail.
Because it is a ratio, the factor of safety is the same whether you work in ksi, psi, or MPa, as long as the strength and the stress use the same unit. This calculator reports the factor of safety against both the yield strength (when the part starts to deform permanently) and the ultimate strength (when it finally breaks), so you can see both the onset of damage and the true breaking margin.
The four modes
Tensile and bending
For direct tension and for bending, the calculator compares the applied normal stress to the yield and ultimate strengths directly. Bending stress comes from M·c÷I; if you do not have it yet, work it out with the Stress Calculator and bring the number back here.
Shear
Shear strength is lower than tensile strength. Using the distortion-energy (von Mises) relationship, the shear yield is about 0.577 times the tensile yield, so the calculator compares your applied shear stress to that reduced limit.
Combined
When a part sees normal and shear stress at once, the calculator forms the von Mises equivalent stress and compares that to yield:
Factor of safety vs margin of safety
The two ideas are related but answer different questions. The factor of safety is the raw ratio of strength to stress. The margin of safety tells you how much spare capacity you have beyond the target factor you set for the design. A margin of safety of zero means you exactly meet your target; a positive margin means you exceed it.
Engineers quote the margin of safety because a positive number is an instant pass and a negative number is an instant fail against the design requirement, no matter what the target was.
Yield vs ultimate strength
Yield strength is the stress at which a metal starts to deform permanently; pass it and the part is bent for good even after the load is removed. Ultimate strength is the stress at which it actually fractures. Most structural design uses the factor of safety against yield, because permanent deformation usually counts as failure. The factor against ultimate is always larger and tells you how close the part is to breaking apart.
How much factor of safety do you need?
There is no single right answer; it depends on how well you know the loads, the material, and the consequences of failure. These ranges are common starting points for ductile metals:
| Situation | Typical FoS |
|---|---|
| Known steady (static) loads, well-characterized material | 1.5 to 2 |
| Varying or repeated loads | 2 to 3 |
| Shock or impact loads | 3 to 5 or more |
| Uncertain loads or brittle material | 3 to 4+ |
Stress concentration and derating
Holes, notches, fillets, and sharp steps raise the local stress well above the average. The stress concentration factor Kt multiplies the applied stress to account for this, so the factor of safety is taken at the worst point, not the nominal section. Temperature and corrosion both cut a material’s usable strength; the derating fields let you knock a percentage off the yield and ultimate before the factor of safety is worked out.
Frequently asked questions
Not necessarily. A very high factor usually means more weight, material, and cost. Good design balances safety against efficiency by matching the factor to how well the loads and material are known.
For ductile metals, design to the yield strength so the part never deforms permanently. The ultimate figure is a useful secondary check on how far you are from fracture.
The applied stress is greater than the material strength, so the part is predicted to fail under the stated load. Reduce the load, add material, or choose a stronger material.
No. A static factor of safety does not protect against cyclic loading, which can fail far below yield. For repeated loads, design against the endurance limit and the stress range.