This spun off many modern words, including "calculate" (use stones for mathematical purposes), and "calculus", which came to be used, in the 18th century, for accidental or incidental mineral buildups in human and animal bodies, like kidney stones and minerals on teeth.Tartar, on the other hand, originates in Greek as well (tartaron), but as the term for the white encrustation inside casks, aka potassium bitartrate commonly known as cream of tartar. This came to be a term used for calcium phosphate on teeth in the early 19th century. Calculus composition
Calculus is composed of both inorganic (mineral) and organic (cellular and extracellular matrix) components. The mineral proportion of calculus ranges from approximately 40–60%, depending on its location in the dentition, and consists primarily of calcium phosphate crystals organized into four principal mineral phases, listed here in order of decreasing ratio of phosphate to calcium:

whitlockite, Ca9(Mg,Fe)(PO4)6(PO3OH)
hydroxyapatite, Ca5(PO4)3OH
octacalcium phosphate, Ca8H2(PO4)6 · 5 H2O
and brushite, CaHPO4 · 2 H2OThe organic component of calculus is approximately 85% cellular and 15% extracellular matrix. Cell density within dental plaque and calculus is very high, consisting of an estimated 200,000,000 cells per milligram. The cells within calculus are primarily bacterial, but also include at least one species of archaea (Methanobrevibacter oralis) and several species of yeast (e.g., Candida albicans). The organic extracellular matrix in calculus consists primarily of proteins and lipids (fatty acids, triglycerides, glycolipids, and phospholipids), as well as extracellular DNA.
Sub-gingival calculus formation and chemical dissolution
Sub-gingival calculus is composed almost entirely of two components: fossilized anaerobic bacteria whose biological composition has been replaced by calcium phosphate salts, and calcium phosphate salts that have joined the fossilized bacteria in calculus formations. The initial attachment mechanism and the development of mature calculus formations are based on electrical charge. Unlike calcium phosphate, the primary component of teeth, calcium phosphate salts exist as electrically unstable ions. The following minerals are detectable in calculus by X-ray diffraction: brushite (CaHPO4 · 2 H2O), octacalcium phosphate (Ca8H2(PO4)6 · 5 H2O), magnesium-containing whitlockite (Ca9(Mg,Fe)(PO4)6(PO3OH)), and carbonate-containing hydroxyapatite (approximately Ca5(PO4)3OH but containing some carbonate).The reason fossilized bacteria are initially attracted to one part of the subgingival tooth surface over another is not fully understood; once the first layer is attached, ionized calculus components are naturally attracted to the same places due to electrical charge. The fossilized bacteria pile on top of one another, in a rather haphazard manner. All the while, free-floating ionic components fill in the gaps left by the fossilized bacteria. The resultant hardened structure can be compared to concrete; with the fossilized bacteria playing the role of aggregate, and the smaller calcium phosphate salts being the cement. The once purely electrical association of fossilized bacteria then becomes mechanical, with the introduction of free-floating calcium phosphate salts. The "hardened" calculus formations are at the heart of periodontal disease and treatment.