Hardness describes a material’s resistance, but its measurement varies fundamentally depending on what is being tested. There is no single unit for hardness because the term applies to three distinct scientific concepts: mechanical resistance, mineralogical scratch resistance, and chemical concentration. Engineers, geologists, and chemists use different methods and corresponding scales because the physical property being measured is unique in each application.
Measuring Material Resistance
Mechanical hardness, or indentation hardness, primarily concerns engineering materials such as metals, alloys, plastics, and ceramics. This type of hardness is defined by a material’s ability to resist permanent deformation when a defined force is applied by a rigid object, known as an indenter. The testing process involves pressing a precisely shaped indenter into the material’s surface with a specific load, then measuring the resulting impression.
The Brinell Hardness Test (HB) uses a large, hardened steel or tungsten carbide ball pressed into the surface with a significant load, often 3,000 kilograms of force. The hardness number is calculated based on the load applied divided by the surface area of the spherical indentation. This result is technically expressed in units of pressure, such as kilograms-force per square millimeter (kgf/mm²), but the final number is treated as a dimensionless index followed by the scale designation.
The Vickers Hardness Test (HV) provides a broader, more consistent scale, making it applicable to a wider range of materials, including very hard ones. This method utilizes a diamond indenter shaped like a square-based pyramid, which produces a clean, small indentation. The Vickers Hardness Number is calculated by dividing the applied load by the surface area of the indentation, and it is also often expressed in kgf/mm².
The Rockwell Hardness Test is the most commonly used in industrial settings due to its speed and simplicity. Instead of measuring the indentation area, the Rockwell test measures the depth of the penetration caused by the indenter. The final Rockwell number is a dimensionless value derived from the difference in penetration depth between an initial minor load and a subsequent major load. The Rockwell method is divided into multiple scales, such as HRC for hardened steels and HRB for softer metals, because no single indenter or load covers the entire range of material hardness. Each scale uses a different combination of indenter shape and test force, resulting in an index specific to that particular scale.
The Mineral Scratch Resistance Scale
Mineralogical hardness focuses on scratch resistance, a property distinct from the mechanical resistance to indentation. This is best exemplified by the Mohs scale of hardness, which is a simple, qualitative ordinal ranking from 1 to 10. Developed by German mineralogist Friedrich Mohs, this scale is based on the ability of one material to visibly scratch another, comparing the strength of the chemical bonds within the crystal lattice.
The scale uses ten reference minerals, with Talc assigned a hardness of 1, representing the softest material, and Diamond assigned a 10, representing the hardest naturally occurring substance. If an unknown mineral can be scratched by Quartz (Mohs 7) but not by Orthoclase (Mohs 6), its hardness is determined to be between 6 and 7.
The Mohs scale is not linear, meaning the difference in hardness between two consecutive numbers is not uniform. For example, Diamond (10) is many times harder than Corundum (9). This qualitative approach is suited for geology and mineral identification, where the simple comparison of resistance to abrasion is the primary concern.
Quantifying Water Quality Hardness
Chemical hardness, or water hardness, measures the concentration of dissolved mineral ions in a liquid, having nothing to do with physical resistance. This property is mainly caused by multivalent metal cations, primarily calcium (\(\text{Ca}^{2+}\)) and magnesium (\(\text{Mg}^{2+}\)) ions, dissolved in the water supply. Water hardness measurement is a concentration measurement, leading to the use of several distinct quantitative units globally.
The most common modern unit is parts per million (ppm), or equivalently milligrams per liter (\(\text{mg}/\text{L}\)), typically expressed in terms of Calcium Carbonate (\(\text{CaCO}_{3}\)) equivalents. Since one liter of water weighs approximately one million milligrams, 1 ppm means 1 milligram of dissolved mineral per liter of water. This metric is a direct measure of mass concentration used for environmental and plumbing applications.
In the United States, an older unit called grains per gallon (GPG) is still frequently used, particularly in the water treatment and softening industry. One grain represents a specific mass of \(\text{CaCO}_{3}\) dissolved in one US gallon of water. To convert between the two, one grain per gallon is approximately equal to 17.1 parts per million.
Another unit often encountered in Europe is the German degree of hardness (\(\text{°dH}\)), which represents a different standard of mineral concentration. One German degree of hardness is roughly equivalent to 17.8 ppm. All these units fundamentally measure the same chemical property: the amount of specific dissolved ions in the water.
Why Different Hardness Measurements Exist
The reason multiple, seemingly unrelated measurements exist under the umbrella term of “hardness” is due to the vastly different physical and chemical processes being assessed. Each measurement is hyper-specific to the application it was designed for, and no single unit could accurately describe all three properties.
Mechanical hardness scales, like Rockwell and Vickers, measure the bulk material’s resistance to plastic deformation under compressive force, which is a function of the material’s internal microstructure and yield strength. Mineralogical hardness, as defined by the Mohs scale, measures the strength of the atomic bonds at the material’s surface, determining its resistance to a physical scratch. These are two distinct forms of physical resistance.
Water hardness, by contrast, is not a measure of physical resistance, but a chemical quantification of dissolved ions in a solution. The unit must therefore be a measure of concentration, such as parts per million. Trying to measure the concentration of calcium ions with a Brinell indenter is impossible, just as measuring a steel beam’s yield strength using a water concentration unit is impossible. The appropriate unit for hardness is completely dependent on the specific scientific discipline and the unique property being investigated.