In the linear elastic range of a uniaxial stress–strain curve, stress is proportional to strain:

$$\sigma=E\varepsilon.$$

The proportionality constant $E$ is Young's modulus.

Stiffness of a material

Young's modulus measures how much stress is required to produce a given elastic strain. A material with a larger $E$ deforms less under the same uniaxial stress.

Because strain is dimensionless, $E$ has the same units as stress.

Material property versus component stiffness

Young's modulus describes the material itself. The stiffness of an actual bar, beam or structure also depends on its geometry and boundary conditions.

For example, two bars made from the same material have the same $E$ but can extend by different amounts if their lengths or cross-sectional areas differ.

Limits of the linear model

The relation $\sigma=E\varepsilon$ applies only where the stress–strain response is approximately linear and elastic. Beyond that region, a constant Young's modulus no longer describes the full constitutive response.