Water Hardness Calculator – Total Hardness, GH/KH and Scaling Tendency
Water hardness is the amount of dissolved calcium and magnesium in water, and this calculator turns the numbers on a water report, a test strip or an EDTA titration into every common unit at once. It also splits temporary and permanent hardness, sizes a water softener and estimates whether the water will scale a kettle using the Langelier Saturation Index.
What “hardness as CaCO₃” means
Hardness is a count of divalent ions. One millimole of Ca²⁺ and one millimole of Mg²⁺ each count as one millimole of hardness, and labs report the total as if it were all calcium carbonate. Each ion is converted with the ratio of molar masses:
TH = Ca × (100.086 / 40.078) + Mg × (100.086 / 24.305) ≈ 2.497·Ca + 4.118·Mg
That is why every hardness unit is a fixed multiple of one number, the mmol/L of Ca²⁺ + Mg²⁺. Water with 52 mg/L calcium and 11 mg/L magnesium has 1.750 mmol/L of hardness, which is 175.2 mg/L as CaCO₃.
gpg, ppm, °dH, °fH and °e
- mg/L or ppm as CaCO₃: used by utilities and labs. For fresh water, ppm and mg/L are equal.
- gpg (grains per US gallon): the water-softener unit in North America;
1 gpg = 17.12 mg/L. - °dH (German degree): 10 mg CaO per litre, the unit on aquarium GH and KH kits;
1 °dH = 17.85 mg/L. - °fH (French degree): 10 mg CaCO₃ per litre. °e (Clark): one grain per imperial gallon, 14.25 mg/L.
Published tables round these to 5.6, 10, 7.02 and 5.85 per mmol/L. The calculator derives them from real molar masses and the exact grain and gallon definitions, so its last digit can differ slightly.
Reading a water report
Reports list either “Calcium (Ca), mg/L” or “Calcium hardness as CaCO₃, mg/L”. The second is about 2.5 times larger for the same water, so choose the unit that matches the line on your report. If the report gives total hardness and calcium only, the calculator derives magnesium from the difference.
Temporary vs permanent hardness
Alkalinity, mostly bicarbonate, is what lets hardness come out of solution when water is heated: Ca²⁺ + 2 HCO₃⁻ → CaCO₃↓ + CO₂ + H₂O. The part of the hardness matched by alkalinity is carbonate (temporary) hardness; the rest, balanced by sulfate or chloride, is non-carbonate (permanent) hardness and stays dissolved on boiling. When alkalinity exceeds hardness, the extra bicarbonate is paired with sodium or potassium, which is why an aquarium KH can read higher than GH.
The EDTA titration
In the classic lab method a sample is buffered to pH 10, Eriochrome Black T is added and EDTA is run in until the colour turns from wine-red to blue. EDTA binds Ca²⁺ and Mg²⁺ one to one, so TH = (V − blank) × c × 100.086 × 1000 / V_sample. A second titration at pH 12–13, where magnesium precipitates as Mg(OH)₂, measures calcium alone; magnesium is the difference.
Why kettles scale when cold pipes don’t
The LSI compares the water’s pH with its saturation pH, LSI = pH − pHs. The saturation pH falls as temperature rises, so the same water can be near balance at 15 °C and scale-forming in a 60 °C water heater. The chart shows that curve, and heating also drives off CO₂, which raises the pH and makes real scaling a little worse.
Setting a water softener
Softeners are set in grains per gallon. Dissolved iron uses up resin capacity too, so guides add about 3–5 gpg for each mg/L of iron and round up. Dividing the softener’s rated capacity by the daily load (hardness × people × daily use) gives the regeneration interval.
Looking for Mohs, Vickers or Rockwell numbers instead? Those measure the hardness of solids; use the Hardness Scale Converter.