How this calculator works
Young's modulus is the elastic axial stress-strain slope. A single pair assumes the elastic line passes through zero. Geometry mode calculates engineering stress and strain from the original area and gauge length. Curve mode fits a straight line with an intercept by ordinary least squares; supply paired stress values in MPa and strain fractions. Choose the elastic segment yourself. A high fit R-squared alone does not prove that the selected interval is elastic.
Formula
E = sigma/epsilon = F L0/[A(Lf-L0)]; fitted E = sum((epsilon-mean epsilon)(sigma-mean sigma))/sum((epsilon-mean epsilon)^2).
Worked example
A stress of 100 MPa at strain 0.0005 gives E = 200 GPa. Data at strains 0, 0.001 and 0.002 with stresses 5, 205 and 405 MPa fit the same modulus and a 5 MPa intercept.
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Frequently asked questions
Should the fit pass through zero?
This fit includes an intercept to reveal an offset. A single stress-strain pair instead assumes a zero intercept.
What strain units belong in the lists?
Use fractions: 0.001 means 0.1%. Stress list values are explicitly in MPa.
Can I fit the plastic region?
The tool will return a slope, but it would describe that chosen interval rather than the elastic Young's modulus.