Ion Concentration as CaCO₃ Equivalent

A water analysis lists a dozen ions with a dozen different atomic weights, and you cannot add or subtract them directly — 20 mg/L of calcium and 20 mg/L of sodium are not the same amount of chemistry. Expressing everything "as CaCO₃" fixes that by converting each ion to the mass of calcium carbonate that carries the same number of charge equivalents. Calcium carbonate has a molar mass of 100.09 and a valence of 2, so its equivalent weight is 50.04 g/eq; divide that by the ion's own equivalent weight and you have the factor. Calcium (EW 20.04) gets 2.497, magnesium (12.15) gets 4.118, sodium (23.0) gets 2.18, bicarbonate (61.0) gets 0.82, and sulphate (48.03) gets 1.04. Forty mg/L of Ca²⁺ becomes 40 × 2.497 = 99.9 mg/L as CaCO₃.

Once every ion is on the CaCO₃ scale you can do the things that make an analysis useful: check that cations balance anions to within a few percent (the classic sanity test on any lab report), split total hardness into carbonate and non-carbonate fractions by comparing hardness to alkalinity, and size a softener or a dealkalizer directly from the numbers. The trap is the word "equivalent" — the divisor is the equivalent weight, molar mass divided by charge, not the molar mass. Using 40.08 for calcium instead of 20.04 halves every hardness figure you produce.