Water Hardness Converter (ppm, gpg, °dH, °fH, °e)

Every water hardness unit against every other — mg/L as CaCO3, grains per gallon, German, French and Clark degrees, mmol/L and meq/L — with the factors computed from the grain and the molar masses, and the WHO, British and German classification bands side by side, because they disagree.

One number, written eight ways

Every hardness unit, and what one of it is worth

The same water, classified by three authorities

What “as CaCO3” means, and why the conversions are exact

Seven units, three verdicts, one number

Hardness units are national conventions, and that is the whole reason this page can answer something a search engine cannot. Not one of them is a unit of a physical quantity. They are seven or eight different ways of writing down the same agreed number, each invented in a different country for a different trade, and converting between them is exact once you know which one you are holding.

What the number actually is. Hardness is the total concentration of divalent metal cations in the water — in practice calcium and magnesium, with traces of strontium and iron. Those two have different molar masses, 40.078 and 24.305, so adding up their masses would mean nothing; what matters is how many of them there are. So every hardness unit in the world expresses the total as the concentration of calcium carbonate that would carry the same number of equivalents. Your water contains no calcium carbonate in that form — if it did it would be scale, not water — and the convention is none the worse for that. It is a unit of account, and it is what makes 40 mg/L of calcium and 24.3 mg/L of magnesium both count as 100 mg/L of hardness.

Then each country picked a different way of writing it. The United States uses mg/L as CaCO3, identical to ppm, and softener ratings in grains per US gallon — one grain of 64.798 91 mg in 3.785 411 784 L, which is 17.118 mg/L. Britain used the Clark degree, a grain in an imperial gallon, 14.254 mg/L. France counts tens of milligrams of the carbonate: one °fH is 10 mg/L. Germany counts tens of milligrams of the OXIDE, so one °dH is 10 mg/L of CaO, which as CaCO3 is 17.848 mg/L. Chemists use mmol/L, and older European work mval/L, which is the milliequivalent under another name: half a millimole, because calcium is divalent. Every factor on this page was computed from the grain, the gallon and the IUPAC atomic weights rather than copied off a chart, and each agrees with the published cross-conversion tables to better than a tenth of a per cent.

And then — this is the part that surprised us — they picked different boundaries too. The WHO and the US Geological Survey publish identical bands: soft below 60 mg/L, moderately hard 60 to 120, hard 120 to 180, very hard above 180. Britain’s Drinking Water Inspectorate publishes soft up to 100, slightly hard 100 to 150, moderately hard 150 to 200, hard 200 to 300, very hard above 300. Germany’s legal bands, set by the Wasch- und Reinigungsmittelgesetz and republished annually by every water supplier, are weich below 1.5 mmol/L, mittel 1.5 to 2.5, hart above 2.5 — which in mg/L is 150.1 and 250.2. So water at 200 mg/L is VERY HARD to the WHO, HARD in London and MEDIUM in Berlin, with nothing about the water having changed. The classification dropdown above exists because of that, and the third table lays all three side by side.

What the number is good for. Setting a dishwasher or a softener, which is the commonest reason anybody looks this up, and the unit the appliance asks for depends on where it was designed — °dH or mmol/L in Germany, °fH in France, grains per gallon in the United States. Mixing up °dH and °fH is a factor of 1.78 in the direction of under-dosing. Beyond that: hardness is what scales a kettle and an immersion heater, what stops soap lathering (the calcium precipitates it as scum), and what a softener is sized against. It is worth knowing that the WHO sets no health-based guideline value for hardness at all — its background document says there are insufficient data to suggest either a minimum or a maximum — so these bands describe nuisance rather than safety, and soft water carries its own separate concern about dissolving plumbing metals.

The other page in this section, the gas concentration converter, has the same structure: a conversion that is exact once you have supplied the one thing only you know.

Frequently asked questions

Related calculators

References

1. U.S. Geological Survey. Hardness of Water, Water Science School, usgs.gov. Soft 0–60 mg/L as calcium carbonate, moderately hard 61–120, hard 121–180, very hard more than 180. A work of the United States Government.
2. World Health Organization. Hardness in Drinking-water, background document for development of WHO Guidelines for Drinking-water Quality, WHO/HSE/WSH/10.01/10/Rev/1. Publishes the same four bands as USGS — soft below 60 mg/L, moderately hard 60–120, hard 120–180, very hard above 180 — and sets NO health-based guideline value for hardness: “there are insufficient data to suggest either minimum or maximum concentrations of minerals at this time”.
3. Drinking Water Inspectorate (England and Wales). Water Hardness / Hard Water, dwi.gov.uk. The British bands, in mg/L as calcium carbonate: soft up to 100, slightly hard 100–150, moderately hard 150–200, hard 200–300, very hard more than 300. These are not the WHO bands and not the USGS ones.
4. Deutscher Verein des Gas- und Wasserfaches. Härtebereiche für Trinkwasser, dvgw.de, setting out the ranges in the German Wasch- und Reinigungsmittelgesetz (WRMG): weich below 1.5 mmol/L of calcium carbonate, mittel 1.5–2.5, hart above 2.5. Suppliers must tell customers which band their water is in at least once a year.
5. Commission on Isotopic Abundances and Atomic Weights (IUPAC). Abridged Standard Atomic Weights, ciaaw.org. Every molar mass on this page is computed from this table — H 1.0080, C 12.011, N 14.007, O 15.999, F 18.998, S 32.06, Cl 35.45, Ca 40.078 — and none is copied from a conversion chart.
6. National Institute of Standards and Technology. NIST Handbook 44, Appendix C, General Tables of Units of Measurement. The international foot is 0.3048 m exactly, the US liquid gallon is 231 cubic inches exactly, the imperial gallon is 4.546 09 L exactly and the grain is 64.798 91 mg exactly. Every foot-, gallon- and grain-based factor on this page descends from those four.
7. Hard water, Wikipedia, and the unit cross-conversion table in it. Used only as an independent check: every factor this page computes from the grain, the gallon and the molar masses agrees with that table to better than 0.12%, which is the table’s own rounding. Where the two differ the computed value is the one used.