Axial Stress Calculator — Force, Area and Yield Safety Factor
Calculate axial normal stress using axial force and cross-sectional area based on σ = F / A.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Axial load
Allowable stress
Cross-section
Material properties [Optional]
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Axial normal stress formula:
σ = F / A
Rearranged forms:
- F = σ · A
- A = F / σ
Additional material check:
- Safety factor = Re / σ
- Utilization σ [%] = (σ / Re) · 100
where:
- σ — axial normal stress (Pa)
- F — axial force (N)
- A — cross-sectional area (m²)
- Re — yield strength (Pa)
When to use this calculator
When to use this calculator:
- Calculate axial normal stress from a known axial force and cross-sectional area.
- Calculate the required axial force from allowable axial stress and cross-sectional area.
- Calculate the required cross-sectional area from axial force and allowable axial stress.
- Check yield-based safety factor when yield strength is provided from a material selection or custom input.
- Evaluate stress utilization as a percentage of yield strength for the selected load case.
How to interpret the result
Axial normal stress is defined as axial force distributed over the cross-sectional area.
The result depends on axial load and load-carrying area. Increasing axial force increases axial normal stress. Increasing cross-sectional area decreases axial normal stress.
- Safe — safety factor is greater than or equal to 1.5.
- Limit — safety factor is greater than or equal to 1.0 and lower than 1.5.
- Unsafe — safety factor is lower than 1.0.
- Info — yield strength is not available, so only the requested axial stress, force, or area result is returned.
- Invalid — required input data is missing, non-finite, or produces a non-positive result.
The result is used to evaluate whether the calculated axial stress stays below the available yield-strength-based limit.
Calculation example
Example:
A user wants to check the axial stress in a loaded bar and compare it with the selected material yield strength.
- F — Axial force = 10000 N
- A — Cross-sectional area = 0.0001 m²
- Re — Yield strength = 250000000 Pa
σ = 100000000 Pa, safety factor = 2.50, utilization σ = 40.0%.
Assumptions and limitations
- The calculation uses the direct axial relationship between force, stress, and cross-sectional area.
- Cross-sectional area is taken either from the selected section model or from the custom area input.
- Material evaluation is performed only when yield strength is available from the material provider or custom input.
- Safety factor is calculated as yield strength divided by axial normal stress.
- Stress utilization is calculated as axial normal stress divided by yield strength and expressed as a percentage.