In this Factor of Safety (FoS) guide, we will show you how to calculate the safety of a material or component in just a few seconds.
We will also help you understand what Factor of Safety means, and how to use the FoS formula while we’re at it.
What is Factor of Safety?
Why is it important in engineering design?
How to calculate FoS for different materials? Find all the answers here! Plus, we will explore real-world examples and applications to make it easy to understand.
Factor of Safety Calculator
Calculate the safety factor using the formula: FoS = Yield Strength / Working Stress
Factor of Safety Explained
Formula & Concept
The Factor of Safety (FoS) is a measure of how safe a material or component is under a given load. It is calculated as:
FoS = Yield Strength / Working Stress
- Yield Strength: Maximum stress a material can withstand without permanent deformation (MPa)
- Working Stress: Actual stress applied to the material under operating conditions (MPa)
Real-world Applications
| Material | Yield Strength (MPa) | Typical Application |
|---|---|---|
| Steel | 250 | Bridges, beams, structural components |
| Aluminum Alloy | 150 | Aircraft frames, automotive parts |
| Copper | 70 | Electrical wires, plumbing pipes |
| Titanium Alloy | 900 | Aerospace components, medical implants |
| Brass | 200 | Valves, gears, decorative hardware |
Worked Example
Problem: A steel rod has a yield strength of 250 MPa. If the working stress applied is 100 MPa, find the Factor of Safety (FoS).
Step 1: Identify known values
- Yield Strength = 250 MPa
- Working Stress = 100 MPa
Step 2: Apply the formula
FoS = Yield Strength / Working Stress
Step 3: Substitute values
FoS = 250 / 100 = 2.5
Step 4: Interpret the result
The Factor of Safety is 2.5, meaning the rod can theoretically handle 2.5 times the current load before reaching its yield strength.
Answer: FoS = 2.5
Material Comparison Table
| Material | Ultimate Tensile Strength (MPa) | Density (g/cm³) | Approx. Cost ($/kg) | Typical FoS Used |
|---|---|---|---|---|
| Steel | 400-550 | 7.85 | 0.5-1 | 2-3 |
| Aluminum Alloy | 200-400 | 2.7 | 2-3 | 1.5-2.5 |
| Copper | 210-250 | 8.96 | 6-8 | 2-3 |
| Titanium Alloy | 900-1000 | 4.5 | 30-50 | 1.5-2.5 |
| Brass | 300-500 | 8.4-8.7 | 3-5 | 2-3 |
FAQs
Why is FoS important in engineering?
FoS helps engineers make sure materials and structures don’t fail under normal use. It adds a safety margin for unexpected loads or defects.
How do engineers choose FoS?
Engineers choose FoS based on the material, type of load, and safety requirements. For example, bridges and machines usually use FoS between 1.5 and 3.
Can FoS be less than 1?
No. If FoS is less than 1, it means the material is overloaded and likely to fail.