The factor of safety is the ratio of a part’s capacity to the demand placed on it in service. For a structural part it is most often expressed as a strength divided by a stress:
n = S ÷ σ
where S is the relevant strength of the material and σ the working stress. A factor of safety of 2 against yield means the working stress is half the yield strength. For ductile metals, S is usually the yield strength, because permanent deformation is the first outcome that is unacceptable. For brittle materials such as grey cast iron, glass and ceramics, which fracture with little or no yielding, it is the ultimate strength.
In engineering practice, two related terms are worth keeping apart. The design factor is the minimum required, set by the code or standard you specify, by a customer or by company practice. The factor of safety is what a particular design achieves once its stresses are known. A design is acceptable when the factor of safety it achieves is at least the design factor. The rest of this guide covers how that required value is chosen and what it protects against.
Calculating a factor of safety
Take a bracket in S355 structural steel, with a nominal yield strength of 355 MPa in thinner sections, and a peak von Mises stress of 142 MPa under its working load. The factor of safety against yield is
n = 355 MPa ÷ 142 MPa = 2.5
Against a minimum ultimate tensile strength of 470 MPa, the same bracket has a factor of about 3.3 against fracture. Both numbers are correct; which one matters depends on how the part is allowed to fail. Von Mises stress is the usual basis of comparison for ductile metals under combined loading, as explained in our guide to von Mises stress.
The factor can also be expressed in terms of load: the load at which the part fails divided by the working load. In a linear problem the two definitions give the same number, because stress is proportional to load. In a non-linear problem they do not. A thin panel can show a low stress and an apparently large factor against yield, yet buckle at 1.4 times its working load. Where buckling, plasticity or changing contact are involved, a factor based on load is the more meaningful one.
Which failure mode the factor applies to
A factor of safety only means something when it is tied to a failure mode, and one part can need several:
- Yield, for ductile parts where permanent set is unacceptable.
- Ultimate strength, for brittle materials, or as a second criterion for ductile parts where some yielding is tolerated but rupture is not.
- Buckling, for slender struts, thin walls and shells under compression or shear.
- Fatigue, for parts under repeated load, where the factor applies to fatigue strength at the required life, or to the life itself. See fatigue analysis.
- Deflection, where a part fails its function by moving too far long before it is overstressed.
- Creep, for metals at high temperature and many plastics under sustained load.
A generous factor against yield says nothing about fatigue. Many service failures occur in parts with healthy static factors whose cyclic loads were never assessed.
Typical factors of safety by application
There is no universal value. The code or standard you specify takes precedence wherever one applies, and many codes split the factor into partial factors on loads and on material resistance rather than using one overall number. As general guidance, values in these ranges are commonly seen:
| Application or situation | Factor commonly used | Why it sits there |
|---|---|---|
| Aircraft and spacecraft structure | Commonly 1.25 to 1.5, applied to the maximum expected load | Weight is critical, and loads, materials, manufacture and inspection are tightly controlled |
| Machine parts with well-defined loads and well-known materials | About 1.5 to 2 against yield | Loads can be calculated with confidence and materials are well characterised |
| General engineering in an ordinary environment | About 2 to 2.5 against yield | Average materials, and loads that can be estimated with reasonable confidence |
| Brittle materials | About 2.5 to 3 against ultimate strength, more under uncertain conditions | Little warning before fracture and wider scatter in strength |
| Uncertain loads, untried materials or harsh environments | Often 3 to 4 or more | The factor has to absorb what is not known |
| Lifting accessories such as chains and slings | Often 4 to 7 against breaking load, depending on type | Wear, misuse, dynamic loading and a severe consequence of failure |
Pressure equipment is typically handled differently again: the code sets an allowable stress as a fraction of both the yield and the ultimate strength, and the lower of the two governs.
Factor of safety vs margin of safety
Margin of safety expresses the same information as a surplus rather than a ratio. In its simplest form it is the factor of safety minus one:
MS = (capacity ÷ demand) − 1
A factor of 1.8 is a margin of 0.8, or 80 %. In aerospace, and in other fields that work to a required design factor, the margin is usually calculated with that factor built in:
MS = S ÷ (σ × nd) − 1
For the bracket above, with a required design factor of 1.5 against yield, MS = 355 ÷ (142 × 1.5) − 1 ≈ 0.67. A positive margin means the requirement is met with capacity to spare, zero means it is met exactly, and a negative margin means it is not met. The convention matters: a margin of 0.2 calculated with a design factor of 1.5 corresponds to a factor of safety of 1.8, where the simple convention would read it as 1.2, so any report should state which convention it uses.
What the factor is covering
A factor of safety is a single number standing in for several separate uncertainties:
- Loads. Peak loads in service, misuse, dynamic amplification from shock or vibration, and combinations of loads that occur together.
- Materials. The difference between typical and specified minimum properties, scatter between batches, lower yield strength in thicker sections, temperature, corrosion, and the loss of strength next to welds in heat-treated aluminium alloys.
- Manufacture. Tolerances, residual stress, surface finish, and defects such as porosity in castings.
- Analysis. Simplifications in how the part, its supports and its loads are represented, and stress concentrations that a simple calculation would not reveal.
- Consequence. What happens if the part fails: injury, downtime or recall, and whether the failure would be noticed before it became dangerous.
These compound. If the peak load could be 30 % above its nominal value and the material 15 % below its typical strength, those two alone consume a factor of about 1.5, since 1.3 × 1.15 ≈ 1.5, before manufacture or analysis is considered. Seen this way, a factor of 2 is less generous than it sounds when loads are poorly understood.
Choosing a factor on evidence
Many design teams inherit a factor, often 2 or 3, and apply it to every part. Habit has two costs. Where loads and materials are well understood, it adds mass, material and cost that the design does not need. Where they are not, it gives false confidence, because a factor applied to the wrong load or the wrong failure mode protects nothing.
Consider a bracket designed to a factor of 3 against yield under its own static weight. Mounted on a vehicle, it sees peak vertical accelerations of 3 g in total, including gravity, so its peak stress is three times the static value and its real factor against yield is about 1, before fatigue is even considered. The size of the factor was reasonable; it was applied to the wrong load.
An evidence-based choice works the other way round. Define the load cases properly, including handling, misuse and dynamic events. Use specified minimum material properties for the actual grade, thickness and temperature. Identify every relevant failure mode, from yield and buckling to fatigue and deflection. Find the real peak stresses, including those at fillets, holes and joints that simple formulas miss, which our guide to stress concentration factors explains. The factor then has to cover only the uncertainty that remains, and the value chosen can be explained to a customer, an insurer or your own technical director.
That can mean a lower factor and a lighter, cheaper part. It can equally mean a higher factor where analysis reveals a failure mode that habit missed.
When to bring in a specialist
If a part looks heavier than it should be, or a customer is questioning the factor of safety behind a design, the way to settle it is an analysis that sets out the loads, materials and stresses explicitly. SixGate™’s stress analysis reports the factor of safety for each relevant failure mode and load case, against the code or standard you specify. It also shows what to change where the factor is too low, and which material can come out of parts that are stronger than they need to be. Where a section changes, the same team updates the detailed design and drawings and can take the part on into production.