There are three principal operational definitions of hardness:

   Scratch hardness

   Indentation hardness

   Rebound, dynamic or absolute hardness

Scratch hardness

In mineralogy, hardness commonly refers to a material's ability to penetrate softer materials. An object made of a hard material will scratch an object made of a softer material. Scratch hardness is usually measured on the Mohs scale of mineral hardness. Pure diamond is the hardest known natural mineral substance and will scratch any other material. Diamond is therefore used to cut other diamonds; in particular, higher-grade diamonds are used to cut lower-grade diamonds.

The hardest substance known today is aggregated diamond nanorods, with a hardness 1.11 times diamond.

Estimates from proposed molecular structure indicate the hardness of beta carbon nitride should also be greater than diamond (but less than ultrahard fullerite). This material has not yet been successfully synthesized.

Indentation hardness

Primarily used in engineering and metallurgy, indentation hardness seeks to characterize a material's hardness; i.e. its resistance to permanent, and in particular plastic, deformation. It is usually measured by loading an indenter of specified geometry onto the material and measuring the dimensions of the resulting indentation.

There are several alternative definitions of indentation hardness, the most common of which are:

A Vickers hardness test

Brinell hardness test (HB)

Janka Wood Hardness Rating

Knoop hardness test (HK) or micro-hardness test, for measurement over small areas

Meyer hardness test

Rockwell hardness test (HR), principally used in the USA

Shore durometer hardness, used for polymers

Vickers hardness test (HV), has one of the widest scales

Barcol hardness test, for composite materials, scale from 0 to 100

There is, in general, no simple relationship between the results of different hardness tests. Though there are practical conversion tables for hard steels, for example, some materials show qualitatively different behaviors under the various measurement methods.

Hardness increases with decreasing grain size. This is known as the Hall-Petch effect. However, below a critical grain-size, hardness decreases with decreasing grain size. This is known as the inverse Hall-Petch effect.

For measuring hardness of nano-grained materials, nano-indentation is used.

Rebound hardness

Also known as dynamic or absolute hardness, rebound hardness measures the height of rebound of an indenter dropped onto a material using an instrument known as a scleroscope. One scale that measures rebound hardness is the Bennett Hardness Scale.