Hardness measures resistance to localized permanent deformation, usually by pressing a harder indenter into a surface under a controlled load.

Different hardness tests use different indenter geometries and measurement rules. Brinell and Vickers methods infer hardness from indentation size; Rockwell methods infer it from penetration depth. Their numerical scales are not interchangeable without an empirical conversion valid for the material range of interest.

For a geometrically similar indentation, hardness has dimensions of stress and can be viewed roughly as

$$H\sim \frac{P}{A},$$

where $P$ is applied load and $A$ is a representative contact or residual indentation area.

For many metals, hardness correlates approximately with tensile or yield strength because both depend on resistance to plastic flow, but the proportionality is material dependent and should not be treated as universal.

Indentation is attractive because it probes a small region and requires little specimen material. That also makes it sensitive to surface preparation, coatings, microstructural heterogeneity and indentation depth.

Hardness is therefore a useful comparative and quality-control property, especially for heat-treated surfaces and wear applications, but it is not a substitute for fracture toughness, ductility or fatigue resistance.