Young's Modulus Calculator
Calculate Young's modulus (elastic modulus) from stress and strain, or from force, area, and deformation measurements. Compare the result with indicative values for common structural materials.
Young's Modulus Calculator
Use matching signs for a compression test: compressive stress/force and strain/shortening should both be negative.
What is Young's Modulus?
Young's modulus (E), also called the elastic modulus or modulus of elasticity, is a fundamental material property that quantifies stiffness. It is defined as the ratio of stress (σ) to strain (ε) in the linear elastic region of a material's stress-strain curve. A higher Young's modulus means the material is stiffer and deforms less under a given load.
Young's modulus has units of pressure (force per unit area), typically expressed in megapascals (MPa) or gigapascals (GPa) in metric, or kips per square inch (ksi) in imperial systems. Strain is dimensionless, being the ratio of change in length to original length.
Common Values for Structural Materials
The table below lists typical Young's modulus values for materials commonly used in structural engineering. These are nominal values; actual modulus can vary with temperature, composition, moisture content, and manufacturing process.
| Material | E (GPa) | E (ksi) | Indicative Strength | Density |
|---|---|---|---|---|
| Structural Steel | 200 | 29,000 | 250-450 MPa | 7850 kg/m³ |
| Stainless Steel | 193 | 28,000 | 170-1000 MPa | 7700-8000 kg/m³ |
| Aluminium (6061-T6) | 68.9 | 10,000 | 240-280 MPa | 2700 kg/m³ |
| Aluminium (General) | 70 | 10,153 | 35-500 MPa | 2700 kg/m³ |
| Concrete (Normal) | 30 | 4,351 | 20-50 MPa (f'c) | 2400 kg/m³ |
| Concrete (High Strength) | 40 | 5,802 | 50-100 MPa (f'c) | 2500 kg/m³ |
| Timber (Softwood) | 11 | 1,595 | 20-40 MPa | 500 kg/m³ |
| Timber (Hardwood) | 16 | 2,321 | 40-80 MPa | 700 kg/m³ |
| Cast Iron (Grey) | 110 | 15,954 | 130-300 MPa | 7200 kg/m³ |
| Copper | 117 | 16,969 | 70-220 MPa | 8940 kg/m³ |
| Glass | 70 | 10,153 | 30-70 MPa (tensile) | 2500 kg/m³ |
| Carbon Fibre (CFRP) | 150 | 21,756 | 1500-3500 MPa | 1600 kg/m³ |
The strength entries are broad context only: their basis varies by material (for example yield, compressive, tensile, or directional composite strength), so they are not directly comparable and must not be inferred from E.
How Young's Modulus is Used in Design
Young's modulus is central to structural design. It combines with the second moment of area (I) to form the flexural rigidity (EI), which governs how much a beam deflects under load. Deflection is inversely proportional to EI: doubling the modulus halves the deflection for the same geometry and loading. Engineers use E to check serviceability limits, compare material options, and predict elastic behaviour in frames, plates, and shells.
Material selection often involves trading off stiffness, strength, weight, and cost. For example, aluminium has roughly one-third the modulus of steel, meaning aluminium members must be deeper or wider to achieve the same stiffness. Carbon fibre composites offer high stiffness-to-weight ratios, making them attractive for specialist applications despite higher cost.
Measuring Young's Modulus
Young's modulus is determined experimentally through uniaxial tensile (or compressive) testing. A specimen of known cross-sectional area and gauge length is loaded while measuring force and extension. The stress-strain curve is plotted, and E is taken as the slope of the initial linear portion. For metals, this linear region is well-defined. For materials like concrete and timber, the curve is nonlinear from the start, so E is typically defined as a secant or tangent modulus at a specified stress level.
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