# Young's Modulus Calculator Solve Young's modulus (modulus of elasticity) in the linear-elastic region using E = σ/ε (Hooke's law). Three directions: modulus E = σ/ε, stress σ = E·ε, strain ε = σ/E. Pick the unknown, supply the other two positive values. Result in MPa with a GPa reading (e.g. steel ≈ 200 000 MPa). > Canonical page: https://elysiatools.com/en/tools/youngs-modulus-calculator - **Category:** Math & Numbers - **Keywords:** young's modulus, elastic modulus, modulus of elasticity, E = sigma/epsilon, Hooke's law, stiffness, linear elastic, stress over strain, mechanics of materials ## Overview The Young's Modulus Calculator uses Hooke's law to solve for modulus E, stress σ, or strain ε in the linear-elastic region. Enter the other two positive values, and get the result in MPa with a GPa reading for modulus. ## Inputs - **Solve for** (select) - **Young's Modulus E (MPa)** (number): Young's modulus in MPa. Required when solving for stress or strain. Typical: steel ≈ 200000–210000, aluminum ≈ 70000. - **Stress σ (MPa)** (number): Normal stress in MPa. Required when solving for modulus or strain. - **Strain ε** (number): Dimensionless strain (ΔL/L₀). Required when solving for modulus or stress. Typically very small (1e-4 – 1e-3). - **Decimal Places** (number) ## When to use - Calculate Young's modulus from measured stress and strain. - Find stress when the modulus and strain are known. - Determine strain from a material's modulus and applied stress. ## How it works - Choose whether to solve for modulus E, stress σ, or strain ε. - Enter the other two values in MPa and dimensionless strain units. - The calculator applies E = σ/ε, σ = E·ε, or ε = σ/E. - View the formatted result with the selected number of decimal places. ## Use cases - Estimate material stiffness from tensile-test stress and strain measurements. - Calculate expected stress for a known modulus and small elastic strain. - Check engineering and mechanics-of-materials calculations using consistent MPa inputs. ## Frequently asked questions ### What formula does the calculator use? It uses Hooke's law in the linear-elastic region: E = σ/ε. ### What units should I use for Young's modulus and stress? Enter both Young's modulus and stress in MPa. The modulus result also includes a GPa reading. ### What unit is used for strain? Strain is dimensionless and is entered as a ratio such as 0.001. ### Which values are required? Enter the two known positive values needed for the selected calculation direction. ### Can this calculator be used beyond the elastic region? No. The calculation is intended for the linear-elastic region where Hooke's law applies. ## Related tools - [BCA Assay Calculator (Protein Standard Curve)](https://elysiatools.com/en/tools/bca-assay-calculator): Least-squares A562 curve fit, back-calculated unknowns with dilution factor, extrapolation flags, and detergent/reducing-agent compatibility notes. Educational use only. - [Bradford Assay Calculator (BSA Standard Curve)](https://elysiatools.com/en/tools/bradford-assay-calculator): Least-squares BSA curve, back-calculated unknowns with dilution factor, extrapolation flags, and protein-specific dye-response caveats. 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