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Young's Modulus from Stress and Strain — result sheet
Calculate tensile or compressive Young's modulus from force, cross-sectional area, original length, and extension.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: stress = F/A; strain = ΔL/L₀; Young's modulus E = stress/strain = F·L₀/(A·ΔL).
Young's modulus is the ratio of axial stress to axial strain in the linear elastic range. Using millimetres for both area and length makes stress naturally appear in N/mm², numerically equal to MPa; the calculator then returns the same modulus in GPa and a simple axial stiffness reference F/ΔL.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Axial force — N; minimum -1000000000; maximum 1000000000
- Cross-sectional area — mm²; minimum 1.0E-6; maximum 1000000000
- Original length — mm; minimum 1.0E-6; maximum 1000000000
- Axial extension — mm; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Axial force | 1000 |
| Cross-sectional area | 100 |
| Original length | 1000 |
| Axial extension | 0.05 |
Stress = 10 MPa, strain = 0.00005, and Young's modulus = 200 GPa.
Assumptions and limits
- Force and extension have matching tension or compression signs and the material is being evaluated in a small, linear-elastic deformation range.
- The cross-section is uniform, the force is axial, and shear, bending, plasticity, necking, and temperature effects are ignored.
- The result is an elastic modulus estimate from entered measurements, not a material certification or structural design approval.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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