Average axial stress
σ = P/A
Axial force divided by original cross-sectional area.
Stress & Strain Calculator
Calculate average axial stress, engineering strain, and the elastic modulus implied by the entered load and deformation.
Access: Free to use, no installation, and No account required.
Inputs
Average axial stress assumes uniform load distribution. Stress concentrations, nonlinear material response, Poisson effects, necking, buckling, residual stress, and multiaxial stress are not included.
Results
Axial stress and engineering strain
Average normal stress is σ = P/A and engineering strain is ε = ΔL/L. When the response is linear elastic, the ratio σ/ε is Young’s modulus.
Engineering reference
Stress & Strain Calculator: background and worked detail
Use the Stress & Strain Calculator to estimate average axial normal stress, engineering strain, microstrain, and the implied Young's modulus from axial force, cross-sectional area, deformation, and original length.
Engineering stress, strain, and modulus
Average axial stress is force divided by original cross-sectional area, and engineering strain is change in length divided by original length. In the linear-elastic region, their ratio is Young's modulus.
Uniform uniaxial stress is an idealization. Real parts can have stress concentrations, multiaxial states, plasticity, residual stress, buckling, connection effects, and nonuniform material response.
Equations used by this calculator
Engineering strain
ε = ΔL/L₀
Change in length divided by original gauge length.
Elastic modulus
E = σ/ε
For a linear-elastic uniaxial response, stress divided by strain gives Young's modulus.
50 kN on 500 mm² with 0.5 mm elongation over 1,000 mm
Use force 50 kN, area 500 mm², deformation 0.5 mm, and original length 1,000 mm.
- σ = 50,000 N / 500 mm² = 100 MPa.
- ε = 0.5/1,000 = 0.0005 = 500 µε.
- E = 100 MPa / 0.0005 = 200 GPa.
Result: The numbers are internally consistent with a typical steel-like elastic modulus.
Linear-elastic region only
Assumptions
- Uniform uniaxial load over the entered area.
- Engineering stress and engineering strain use original geometry.
- E is meaningful only when the entered state represents linear-elastic behavior.
Limitations
- Does not calculate yielding, necking, true stress/strain, Poisson effects, stress concentration, or multiaxial failure.
- A modulus inferred from one noisy or nonlinear data point may not represent material Young's modulus.
Validation checks
Force scaling
Case: Double axial force with area and deformation relation otherwise held for a purely algebraic check.
Expected: Calculated average stress should double.
Unit consistency
Case: Scale force and area by the same factor.
Expected: Calculated stress should remain unchanged.
Stress & Strain Calculator FAQ
What is microstrain?
One microstrain is 10⁻⁶ strain. A strain of 500 µε equals 0.0005.
Can I use this after yielding?
The stress and engineering strain can still be computed, but σ/ε is no longer Young's modulus once the response is nonlinear or plastic.
Is force divided by area always the maximum stress?
No. P/A is the average axial stress. Holes, notches, bending, connections, and local geometry can create much higher local stress.
Where this calculation comes from
Shared with the Mechanical Properties and Failure Workbench, which covers plasticity, fatigue, and fracture.
Open the source workbench →Read calculation and source methodology →