Young's Modulus / Elastic Modulus Calculator
Calculate stress, strain, and deformation using Young's modulus.
Look up elastic modulus values for steel, aluminum, copper, concrete, and other materials.
What Is Young’s Modulus? Young’s modulus (E) is a measure of a material’s stiffness — resistance to elastic deformation under stress. Named after Thomas Young, English scientist, 1807. Definition: E = stress / strain = (F/A) / (ΔL/L₀) Units: GPa (gigapascals) = 10⁹ Pa. Also expressed in psi or ksi.
Stress, Strain, and Hooke’s Law Normal stress: σ = F/A (force divided by cross-sectional area). Normal strain: ε = ΔL/L₀ (elongation divided by original length). Dimensionless. Hooke’s Law: σ = E × ε (linear elastic region only). Deformation: ΔL = F × L₀ / (A × E) Valid only below the yield strength — permanent deformation begins beyond that point.
Typical Young’s Modulus Values Steel (structural A36): E ≈ 200 GPa. Used in buildings, bridges, cars. Stainless steel: E ≈ 193–200 GPa. Aluminum (6061-T6): E ≈ 68.9 GPa — roughly 1/3 of steel. Copper: E ≈ 110–130 GPa. Titanium (Ti-6Al-4V): E ≈ 113.8 GPa — similar stiffness to copper but much lighter. Concrete (in compression): E ≈ 17–31 GPa (varies with strength grade). Douglas Fir (wood, along grain): E ≈ 13 GPa. Glass: E ≈ 70–80 GPa. Carbon fiber reinforced polymer: E ≈ 70–200 GPa (along fiber direction). Rubber: E ≈ 0.01–0.1 GPa (very flexible). Bone (cortical): E ≈ 14–20 GPa. Diamond: E ≈ 1,000 GPa — stiffest known material.
Specific Stiffness Often more important than absolute stiffness is E/ρ (Young’s modulus per density): Steel: 26 GPa·m³/Mg. Aluminum: 26 GPa·m³/Mg (same! — why aerospace uses both). Carbon fiber: 100–200 GPa·m³/Mg — lightweight and stiff. Titanium: 26 GPa·m³/Mg (similar to steel/aluminum).
Poisson’s Ratio Lateral contraction when stretched: ν = −(lateral strain) / (axial strain). For most metals: ν ≈ 0.25–0.35. Rubber: ν ≈ 0.5 (nearly incompressible). Shear modulus: G = E / (2(1+ν)). Bulk modulus: K = E / (3(1−2ν)).
Beyond the Elastic Limit Yield strength: stress at which permanent deformation begins. Ultimate tensile strength (UTS): maximum stress before fracture. Young’s modulus tells you about stiffness only — it says nothing about strength. A rubber band is flexible (low E) but can stretch far; a glass rod is stiff (high E) but brittle.
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