Water Hardness Units: Converting ppm, °dH, °Clark and Grains per Gallon

A 280 ppm supply is 15.7 German degrees and 16.4 grains per gallon. How the five hardness scales convert, and why your dishwasher wants the one furthest from the published figure.

Introduction

Water hardness is measured in at least five different units, and your water company, your dishwasher and your water softener are each likely to use a different one. A supply reported as 280 ppm by the utility is 15.7 on the German scale your dishwasher asks for, and 16.4 in the grains an American softener is sized by. Same water, three numbers, no conversion printed anywhere.

What Hardness Actually Measures

Hardness is the concentration of dissolved calcium and magnesium. Because the two contribute differently, every scale expresses the total as an equivalent amount of one reference compound — almost always calcium carbonate, CaCO₃.

That is why figures are written as "mg/L as CaCO₃". It does not mean the water contains that much chalk. It means the measured calcium and magnesium have the same effect as that much calcium carbonate would.

The Five Units

ppm or mg/L as CaCO₃ — the international standard, and the same number in both forms. Also called the American degree.
°fH, French degrees — 10 mg/L CaCO₃ each, so this is just ppm divided by ten.
°dH, German degrees — defined against calcium oxide rather than carbonate, which is where the awkward factor comes from.
°Clark, English degrees — one grain per imperial gallon.
gpg, grains per gallon — one grain per US gallon, standard in American water treatment.

The Conversion Factors

Everything converts through ppm:

1 °fH = 10 ppm
1 °Clark = 14.25 ppm
1 gpg = 17.12 ppm
1 °dH = 17.85 ppm

The two odd numbers are not arbitrary. A grain is 64.79891 mg, so a grain in a US gallon of 3.785 litres is 17.12 mg/L, and the same grain in the larger imperial gallon of 4.546 litres is only 14.25. The German degree is 10 mg/L of calcium oxide, and CaO has a smaller molar mass than CaCO₃, so converting gives 10 × 100.09 ÷ 56.08 = 17.85.

Useful cross-conversions: 1 °dH = 1.04 gpg, which is close enough that the two scales are often mistaken for each other, and 1 gpg = 1.71 °fH.

Where Your Water Sits

The usual classification, with every boundary converted:

Soft, under 60 ppm — under 3.4 °dH, 3.5 gpg, 6 °fH, 4.2 °Clark
Moderately hard, 60 to 120 ppm — 3.4 to 6.7 °dH, 3.5 to 7.0 gpg
Hard, 120 to 180 ppm — 6.7 to 10.1 °dH, 7.0 to 10.5 gpg
Very hard, above 180 ppm — above 10.1 °dH, 10.5 gpg

Much of south-east England runs 250 to 350 ppm, firmly in very hard territory, while most of Scotland and Wales is soft. The ppm figure is the one water companies publish, so it is usually the starting point. Our guide to parts per million covers why 1 ppm is 1 mg/L in water in the first place.

Setting a Dishwasher

This is the conversion most people actually need, and the one most likely to be done wrong.

Dishwasher water softeners are set in °dH, because the appliances are overwhelmingly German-designed. Water companies publish ppm. Divide by 17.85 to get from one to the other.

So a 280 ppm supply is 15.7 °dH, which on most machines is near the top of the scale. Setting it from the ppm figure by mistake would be meaningless, and leaving it at the factory default of around 3 means the softener regenerates far too rarely — which is why glasses go cloudy and the machine scales up even though salt is in the reservoir.

A Trap for Aquarium Keepers

Fishkeeping uses two hardness measurements that look alike and are not interchangeable.

GH, general hardness, is the calcium and magnesium described above. KH, carbonate hardness, measures carbonates and bicarbonates instead, and governs how well the water resists pH swings. Both are commonly quoted in degrees on the German scale, so a reading of 8 could mean either.

They are different quantities, not different units for the same thing, and no factor converts between them. A test kit will say which it measures.

Quick Reference Conversion Table

1 ppm = 0.1 °fH = 0.07 °Clark = 0.058 gpg = 0.056 °dH
1 °fH = 10 ppm
1 °Clark = 14.25 ppm = 1.43 °fH
1 gpg = 17.12 ppm = 1.71 °fH = 0.96 °dH
1 °dH = 17.85 ppm = 1.79 °fH = 1.04 gpg
100 ppm = 5.6 °dH = 5.8 gpg
200 ppm = 11.2 °dH = 11.7 gpg
300 ppm = 16.8 °dH = 17.5 gpg

Common Mistakes Worth Avoiding

Entering ppm where a dishwasher wants °dH

The scales differ by a factor of nearly 18. Divide the published figure by 17.85.

Treating °dH and gpg as the same

They are only 4 percent apart, which makes the error invisible but real at high hardness.

Confusing GH with KH

Different quantities measuring different ions. No conversion exists between them.

Assuming a water company figure is current

Hardness varies with source and season, and many areas are supplied from more than one. Published figures are averages or ranges.

Conclusion

Convert everything through ppm: divide by 10 for French degrees, by 14.25 for Clark, by 17.12 for grains per gallon, and by 17.85 for German degrees. The German scale is the one your dishwasher wants and the one furthest from the published figure, so it is where the mistake usually happens.

Try our milligrams to grams converter for the mass side of these figures.