Water Hardness Calculator (Ca, Mg → CaCO₃)

Understanding the water hardness calculator — concept and principle

Water hardness is mainly the dissolved calcium and magnesium in water. It decides how easily soap lathers, how fast scale builds up in kettles, boilers and pipes, and how hard a softener must work. Laboratory reports usually give calcium and magnesium separately in mg/L; this calculator combines them into total hardness expressed as calcium carbonate (mg/L as CaCO₃), converts it to German degrees and grains per gallon, and classifies it on the US Geological Survey scale.

Ca and Mg add up to 211.59 mg/L as CaCO₃ — past 180, so “very hard”.

How it is calculated

Total hardness (mg/L as CaCO₃) = 2.497 × Ca + 4.118 × Mg, with Ca and Mg in mg/L.
German degrees: °dH = hardness ÷ 17.848 (1 °dH = 10 mg/L CaO = 17.848 mg/L CaCO₃).
Grains per US gallon: gpg = hardness ÷ 17.118 (1 grain = 64.8 mg, 1 gallon = 3.785 L).
USGS class: under 60 soft, 60–120 moderately hard, 120–180 hard, 180 and above very hard (mg/L as CaCO₃).

The principle

Calcium and magnesium have different atomic masses, so 1 mg of each does not represent the same amount of hardness. Expressing both as an equivalent mass of CaCO₃ puts them on a common scale. Each ion carries a charge of 2+, just like the CaCO₃ unit it is compared with, so the conversion factor is the ratio of molar masses: 100.09 ÷ 40.08 = 2.497 for calcium and 100.09 ÷ 24.305 = 4.118 for magnesium. A milligram of magnesium therefore counts for more hardness than a milligram of calcium.

Worked example

Inputs: Ca = 60 mg/L, Mg = 15 mg/L.
Calcium part: 2.497 × 60 = 149.82 mg/L as CaCO₃.
Magnesium part: 4.118 × 15 = 61.77 mg/L as CaCO₃.
Total hardness = 149.82 + 61.77 = 211.59 mg/L as CaCO₃.
German degrees: 211.59 ÷ 17.848 = 11.86 °dH; grains per gallon: 211.59 ÷ 17.118 = 12.36 gpg.
211.59 is above 180, so the USGS class is very hard.

Each point is the calculator re-run with only “Calcium (mg/L)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Calcium (mg/L)	Hardness (mg/L as CaCO₃)
15	99.225
30	136.68
45	174.135
60	211.59
75	249.045
90	286.5
120	361.41

How to read the result

Where does your result fall?

Hard water is not a health hazard, and the World Health Organization has not set a health-based guideline value for hardness. Its effects are practical: scale in heaters and appliances, spots on glassware and more soap needed for washing. Different countries use different class boundaries and units, so compare against the scale used where you live.

Common mistakes

Adding Ca and Mg in mg/L directly without the conversion factors.
Entering results already expressed as CaCO₃ and converting them again.
Confusing total hardness with carbonate (temporary) hardness, which is limited by alkalinity.

Keep in mind: This calculation counts calcium and magnesium only. Other polyvalent ions such as strontium, iron or manganese also contribute slightly, and titration methods such as EDTA measure them together.

Frequently asked questions

What is temporary hardness?

The part of hardness balanced by bicarbonate; boiling removes it as scale. The rest is permanent hardness.

Do household filters remove hardness?

Ion-exchange softeners and reverse osmosis do; ordinary activated-carbon filters do not.

How do I convert mg/L as CaCO₃ to mmol/L?

Divide by 100.09; 211.59 mg/L is about 2.11 mmol/L.

Sources: US Geological Survey, Water Science School, "Hardness of Water" · APHA, AWWA and WEF, Standard Methods for the Examination of Water and Wastewater, Method 2340 · World Health Organization, Hardness in Drinking-water, background document for the Guidelines for Drinking-water Quality

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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