About the Factor of Safety Calculator
This factor of safety calculator compares what a part can withstand with what it actually carries. Enter the strength — yield or ultimate stress, or a rated breaking load — and the working stress or load, and it returns the factor of safety (FoS = strength ÷ applied). Add the safety factor your design code or company standard requires and it also gives the allowable stress or load, the minimum strength you need, the margin of safety and how much of the allowable capacity is used.
It works for any consistent unit — MPa, psi, ksi, newtons, kilonewtons or pounds — so you can use it for a shaft, bracket, bolt, beam, lifting sling, rope or pressure part. Students use it to check mechanics-of-materials homework; engineers use it as a quick go/no-go check once the stresses are known.
The result is only as good as the inputs: use the right strength for the failure mode (yield for ductile parts, ultimate for brittle parts or rated breaking loads, endurance limit for fatigue) and the peak stress including stress concentrations. Required factors vary widely — from about 1.5 in aerospace structures to 5 or more for lifting gear — so follow the governing standard.
How to use the factor of safety calculator
- 1Pick the unit you are working in (it only labels the results).
- 2Enter the strength or failure load for the relevant failure mode.
- 3Enter the maximum working stress or load in service.
- 4Enter the factor of safety your code or standard requires.
- 5Check the factor of safety, margin of safety and utilization.
Formula and method
The factor of safety is the ratio of the capacity of a part to the demand on it. Using stresses, it is the material strength (yield strength for ductile metals, ultimate strength for brittle materials) divided by the maximum working stress; using loads, it is the failure or rated breaking load divided by the working load. A FoS of 2 means the part could carry twice the current load before failing.
Design codes usually fix a required factor, which gives an allowable stress or load equal to strength ÷ required FoS. The margin of safety, common in aerospace, is strength ÷ (applied × required FoS) − 1: zero means the part exactly meets the requirement and a negative value means it does not. Utilization is the applied value as a percentage of the allowable.
- FoS
- Factor of safety (actual)
- FoS_req
- Required or design factor of safety
- MS
- Margin of safety
- strength
- Yield/ultimate strength or failure load
- applied
- Maximum working stress or load
Worked examples
Steel bracket: 250 MPa yield, 100 MPa working stress, FoS 2 required
FoS = 250 ÷ 100 = 2.5, which beats the required 2.0. The allowable stress is 250 ÷ 2 = 125 MPa, so the bracket uses 80% of it, and the margin of safety is 250 ÷ (100 × 2) − 1 = 0.25.
Lifting rope: 50 kN breaking load, 8 kN load, 5:1 design factor
The rope’s factor of safety is 50 ÷ 8 = 6.25. With a 5:1 design factor its working load limit is 50 ÷ 5 = 10 kN, so the 8 kN load uses 80% of the limit.
Overstressed member: 36 ksi yield, 28 ksi stress, FoS 1.67 required
FoS = 36 ÷ 28 = 1.29, below the required 1.67. The allowable stress is 36 ÷ 1.67 = 21.6 ksi, so the member is at 130% of its allowable and the margin of safety is −0.23; it needs a stronger material (46.8 ksi yield) or a larger section.
Frequently asked questions
What is the factor of safety formula?+
Factor of safety = strength ÷ applied stress, or failure load ÷ working load. A shaft with 400 MPa yield strength carrying 160 MPa has FoS = 400 ÷ 160 = 2.5. Anything below 1 means the part is predicted to fail.
What is a good factor of safety?+
It depends on how well loads and materials are known and the consequences of failure. Typical values: about 1.5 for aircraft structures, 1.5–2 for structural steel against yield, 2–4 for general machine parts, and 5 or more for wire rope and lifting equipment.
What is the difference between factor of safety and margin of safety?+
Factor of safety is the ratio strength ÷ load. Margin of safety expresses how far a design exceeds a required factor: MS = strength ÷ (load × required FoS) − 1. An MS of 0 just meets the requirement; 0.25 means 25% extra capacity beyond it.
Should I use yield or ultimate strength?+
Use yield strength when permanent deformation counts as failure, which is normal for ductile metals. Use ultimate strength for brittle materials like cast iron or glass, or when the rating is a breaking load. Use the endurance limit for parts under cyclic loading.
What is a design factor?+
A design factor is the required factor of safety set before design, often by a code or standard, while the factor of safety is what the finished design actually achieves. Lifting standards often call it the design factor, e.g. 5:1 for wire rope slings.