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, meaning its 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 to 200 GPa. Aluminum (6061-T6): E ≈ 68.9 GPa, roughly a third of steel. Copper: E ≈ 110 to 130 GPa. Titanium (Ti-6Al-4V): E ≈ 113.8 GPa, similar stiffness to copper but much lighter. Concrete (in compression): E ≈ 17 to 31 GPa, varying with strength grade. Douglas Fir (wood, along grain): E ≈ 13 GPa. Glass: E ≈ 70 to 80 GPa. Carbon fiber reinforced polymer: E ≈ 70 to 200 GPa along the fiber direction. Rubber: E ≈ 0.01 to 0.1 GPa, which is why it stretches. Bone (cortical): E ≈ 14 to 20 GPa. Diamond: E ≈ 1,000 GPa, the stiffest known material.
Specific Stiffness Often more useful than absolute stiffness is E/ρ, Young’s modulus divided by density: Steel: 26 GPa·m³/Mg. Aluminum: 26. Titanium: 26. All three land on the same number, which is why aerospace happily uses all of them and picks on other grounds. Carbon fiber: 90 to 130 for common laminates, and higher again for high-modulus fiber. That gap is the whole reason composites took over.
Poisson’s Ratio Lateral contraction when stretched: ν = −(lateral strain) / (axial strain). For most metals: ν ≈ 0.25 to 0.35. Rubber: ν ≈ 0.5, meaning 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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