What is factor of safety (FoS)?

FoS is the ratio of material strength to the actual applied stress. A FoS above 1 indicates the design can carry the load under the assumed conditions.

Should I use yield or ultimate strength?

Use yield strength (Sy) for ductile materials when permanent deformation is the limiting state. Use ultimate strength (Su) for brittle materials or when fracture is the limiting state.

Is factor of safety unitless?

Yes. FoS is a ratio of two stresses (strength and applied stress), so units cancel out.

What are typical target FoS values?

Typical targets vary by industry and uncertainty. For well-controlled, tested components FoS can be 1.2–1.5; for common mechanical designs 1.5–2.0; for high uncertainty or life-safety systems, higher values may be mandated by codes or standards.

How does stress concentration affect FoS?

Applied stress should include local peak stresses (e.g., Kt effects). Using a lower, averaged stress can overestimate FoS.

What happens if applied stress is zero?

FoS tends to infinity mathematically. In practice, verify that your loading and stress computation are correct.

Factor of Safety Calculator

Q: What is margin of safety (MS)?

Margin of Safety is MS = FoS − 1. A positive MS indicates additional capacity beyond the working load.

Data Source and Methodology

Authoritative Sources:

J. E. Shigley, C. R. Mischke, R. G. Budynas, Shigley's Mechanical Engineering Design, 11th ed., McGraw-Hill, 2020. Publisher page
NASA-STD-5001 Rev E (2022), Structural Design and Test Factors of Safety for Spaceflight Hardware. Official NASA standard

All calculations are strictly based on the definitions and formulas provided by these sources. This tool implements the fundamental relationships for Factor of Safety (FoS), Margin of Safety (MS), and Allowable Stress.

The Formula Explained

FoS = Strength / AppliedStress

MS = FoS - 1

σ_allow = Strength / FoS_target

σ = F / A

Select strength as Sy (yield) for ductile design or Su (ultimate) for brittle/fracture-limited design.

Glossary of Variables

Strength (Sy or Su): Material resistance to yielding (Sy) or fracture (Su), in units of stress.
Applied stress (σ): Maximum expected working stress under service loads.
FoS: Factor of Safety, unitless ratio Strength/Applied stress.
MS: Margin of Safety, unitless, MS = FoS − 1.
σ_allow: Allowable stress that meets a chosen target FoS.
FoS_target: Designer’s chosen minimum factor of safety.

How It Works: A Step-by-Step Example

Suppose a ductile steel has yield strength Sy = 250 MPa and the maximum working stress is σ = 120 MPa. You want a target FoS of 1.8.

Compute FoS: FoS = 250 / 120 ≈ 2.083.
Margin of Safety: MS = 2.083 − 1 = 1.083.
Allowable stress for target: σ_allow = 250 / 1.8 ≈ 138.89 MPa.
Status: Since 120 MPa ≤ 138.89 MPa, the design passes the 1.8 target.

Frequently Asked Questions (FAQ)

Is the factor of safety dimensionless?

Yes. It is a ratio of two stresses, so units cancel out.

Which strength should I use?

Use yield strength (Sy) when preventing permanent deformation is critical (ductile materials). Use ultimate strength (Su) when fracture controls (brittle materials) or when required by your code.

What is a typical FoS?

There is no universal value. Common ranges are 1.5–2.0 for general mechanical design, lower for highly controlled and tested systems, and higher for life-safety or high-uncertainty situations. Follow your governing standards.

Does load combination or dynamic effects matter?

Yes. You should include appropriate load factors, dynamic amplification, and stress concentration factors so the applied stress reflects worst-case conditions within your design framework.

What is Margin of Safety?

MS = FoS − 1. A positive MS means reserve capacity beyond the working load; zero means at the limit; negative means overstressed.

Can I mix units?

Enter both strength and stress in the same unit family using the unit menus. The calculator handles conversions consistently.

Where can I learn more?

Consult Shigley’s Mechanical Engineering Design and NASA-STD-5001 for formal definitions and recommended safety factors. For a general overview, see the topic page on factor of safety by reputable institutions.

Tool developed by Ugo Candido. Content verified by Mechanical Engineering QA Team.
Last reviewed for accuracy on: September 15, 2025.