The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness or rigidity of a material. It quantifies the relationship between the amount of stress applied to a material and the resulting strain (deformation) it experiences.

Mathematically, Young's modulus (E) is defined as the ratio of stress (σ) to strain (ε) within the elastic limit of a material:

E= σ​ / ε

Where:

• E = Young's modulus (modulus of elasticity) measured in Pascals (Pa) or pounds per square inch (psi).
• σ = Stress applied to the material in Pascals (Pa) or psi.
• ε = Strain or deformation (unitless).

Young's modulus helps engineers and scientists understand how much a material will deform under stress, enabling them to predict how materials will behave under different conditions. Materials with high Young's modulus are stiffer and require more stress to induce deformation, while materials with lower Young's modulus are more flexible and deform more readily under stress.