120 water hardness cells — 150 ppm is 8.4 °dH and 8.76 gpg

ppm counts the hardness as if it were all chalk

Hardness comes mostly from calcium and magnesium ions, and writing the two separately makes waters impossible to compare. The convention is therefore to express the lot as calcium carbonate, CaCO₃, in a single number — that is ppm, and since it means one milligram in one litre of water it is the same figure as mg/L. All six units are just that one number written differently, which is why any of them converts into any other.

The conversion factors fall out of the definitions

The German degree is defined as one degree per 10 mg/L of calcium oxide, CaO. Because the reference substance is CaO and not CaCO₃, the molar mass ratio 100.09 ÷ 56.08 has to come in, which is why one °dH is 17.85 ppm. The French degree is defined as 10 mg/L of CaCO₃ — the same substance as the base — so its factor is exactly 10. Both read "one degree per 10 mg/L", and the 1.78-fold gap between them is entirely that substance. The English degree is one grain of CaCO₃ in an imperial gallon (14.25 ppm), the American gpg is the same grain in a US gallon (17.12 ppm), and mmol/L is simply the molar mass, 100.09. This chart builds every factor from those definitions instead of copying them down.

Where soft ends and hard begins depends on the standard

The conversions are fixed; the grades are a choice. This chart draws its lines at the widely quoted 60, 120 and 180 ppm — meaning they are our approximation. The German detergent law, WRMG, draws its own at 1.5 and 2.5 mmol/L, that is 150.1 and 250.2 ppm, or 8.4 and 14 °dH. A 150 ppm water is therefore "hard" on this chart and "soft" under that law — the water did not change, the ruler did. Near a boundary, do not settle the question here: read the standard your appliance or your country actually uses.

Reading a manual written for another country

You need this conversion when buying a softener, a filter jug, a dishwasher or an espresso machine. A German dishwasher asks you to enter the hardness in °dH, an American softener rates its capacity in gpg, and a French coffee machine sets its filter interval in °fH. The same tap water becomes three numbers — 8.4, 8.76 and 15 — so typing the manual’s scale straight in means changing filters too often or missing the scale build-up. Your own figure is on the water utility’s quality report under hardness, usually in mg/L, which is ppm unchanged.

soft0–60 ppm

moderately hard60–120 ppm

hard120–180 ppm

very hard180+ ppm

Worth knowing

• ppm (mg/L CaCO₃) is the base, and every other unit is a fixed multiple of it.
• °dH is ppm ÷ 17.85, gpg is ppm ÷ 17.12, °fH is ppm ÷ 10, °e is ppm ÷ 14.25 and mmol/L is ppm ÷ 100.09.
• °dH and °fH both read "one degree per 10 mg/L", yet differ 1.78-fold because one counts CaO and the other CaCO₃.
• Grade boundaries differ between standards — the 60, 120 and 180 ppm on this chart are our chosen approximation.