Water Hardness Calculator
Total, calcium and magnesium hardness from Ca²⁺ and Mg²⁺ (mg/L, mmol/L or as CaCO₃), from an EDTA titration or from a total you already have — in mg/L as CaCO₃, ppm, gpg, °dH, °fH, °e, mmol/L and meq/L, with the hardness class on US, WQA and German scales, temporary vs permanent hardness and water-softener sizing.
How it works
hardness (mg/L CaCO₃) = 2.497 × Ca (mg/L) + 4.118 × Mg (mg/L); EDTA: hardness = M × V(EDTA, mL) × 100,090 ÷ V(sample, mL); 1 °dH = 17.85 mg/L; 1 °fH = 10 mg/L; 1 gpg = 17.12 mg/L; 1 °e = 14.25 mg/L; 1 mmol/L = 100.09 mg/L; softener load (grains/day) = (gpg + 4 × iron mg/L) × US gal/day
Hardness is the total of dissolved calcium and magnesium, expressed as the equivalent mass of calcium carbonate so the two can be added. The factors are the ratio of CaCO₃’s molar mass to each metal’s (100.09/40.08 and 100.09/24.31). You can start from calcium and magnesium in mg/L, mmol/L, meq/L or as CaCO₃, from an EDTA titration, or from a total you already have in any unit, and get the result in every common unit. An EDTA titration at pH 10 counts calcium and magnesium together; a second titration at pH 12–13 counts calcium alone, and the difference is magnesium. The part balanced by bicarbonate alkalinity is “temporary” hardness, which precipitates as scale on boiling, while the rest is “permanent”. Hardness bands differ by country, so the calculator shows the US (USGS/WHO), Water Quality Association and German classes. For a water softener, multiply hardness in grains per gallon (plus about 4 gpg for each mg/L of iron) by daily use. That gives the grains removed per day; times the days between regenerations, plus a 20% reserve, gives the capacity to buy.
Worked example
60 mg/L Ca and 15 mg/L Mg: 60 × 2.497 + 15 × 4.118 = 149.8 + 61.8 = 212 mg/L as CaCO₃, which is very hard (11.9 °dH, 12.4 gpg). With 120 mg/L alkalinity, 120 is temporary and 92 permanent. At 400 L a day (105.7 US gal) the softener removes 12.4 × 105.7 ≈ 1,306 grains a day, so a 7-day cycle with a 20% reserve needs about 11,000 grains and a 16,000-grain unit is enough. By titration, 12.40 mL of 0.0100 M EDTA for a 100 mL sample gives 0.01 × 12.40 × 100,090 ÷ 100 = 124 mg/L as CaCO₃.
Frequently asked questions
What is “ppm” hardness?
For practical purposes it is the same as mg/L as CaCO₃. 1 grain per gallon is 17.1 ppm, 1 °dH is 17.8 ppm and 1 °fH is 10 ppm.
Is hard water unhealthy?
No. Calcium and magnesium are nutrients, and WHO sets no health-based limit for hardness. Hardness is a nuisance for appliances, plumbing and soap, not a health issue.
What counts as hard water?
On the US scale used by USGS and WHO, under 60 mg/L as CaCO₃ is soft, 60–120 moderately hard, 120–180 hard and over 180 very hard. The Water Quality Association uses grains per gallon (over 7 gpg is hard), and Germany uses mmol/L (over 2.5 mmol/L, or 14 °dH, is hard).
How do I calculate hardness from an EDTA titration?
Multiply the EDTA molarity by the titre in mL and by 100,090, then divide by the sample volume in mL. 12.40 mL of 0.0100 M EDTA for a 100 mL sample gives 124 mg/L as CaCO₃. Each EDTA binds one Ca²⁺ or Mg²⁺, so the factor is the full molar mass of CaCO₃ (100.09), not half of it.
What size water softener do I need?
Multiply hardness in grains per gallon (add 4 gpg per mg/L of iron) by the gallons used per day, then by the days you want between regenerations, and add about 20%. A family using 300 US gal a day at 15 gpg removes 4,500 grains a day, so a weekly cycle needs about 38,000 grains: a 40,000-grain unit.
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This calculator is for educational purposes. Double-check important results before acting on them.