Modulus of Elasticity Calculator

The modulus of elasticity (E), also called Young's modulus, is a material property that measures stiffness. It is defined as the ratio of stress (force per unit area) to strain (deformation per unit length) in the elastic (linear) region of the material's stress-strain curve. A higher E value means a stiffer material. Steel E = 29,000 ksi; aluminum E = 10,000 ksi; concrete E = 3,000-4,000 ksi; wood E = 1,000-2,000 ksi.

E = Stress / Strain = (F/A) / (dL/L), where F is applied force, A is cross-sectional area, dL is the change in length, and L is the original length. Stress is expressed in psi or MPa; strain is dimensionless (in/in or mm/mm). E is expressed in the same units as stress (psi, ksi, MPa, GPa).

Elastic deformation is reversible. When load is removed, the material returns to its original shape. This occurs in the linear region of the stress-strain curve, where E applies. Plastic deformation is permanent and occurs after the yield strength is exceeded. Engineering structures are designed to remain in the elastic range under service loads.

Poisson's ratio (v) is the negative ratio of transverse strain to axial strain under uniaxial stress. When a material is stretched axially, it contracts laterally. For steel v = 0.3, for concrete v = 0.2. Together with Young's modulus, Poisson's ratio defines isotropic material behavior. The shear modulus G = E / (2(1+v)) and bulk modulus K = E / (3(1-2v)) can be derived from E and v.

Young's modulus is fundamental to structural analysis. Deflection of beams: delta = (5wL^4) / (384EI) for uniformly loaded simply-supported beams. Column buckling load: Pcr = (pi^2 x E x I) / (KL)^2. Spring stiffness: k = AE/L for axially loaded members. E determines how much a structure deflects under load and is required for all finite element analysis models.