What this calculator does
Water hardness is the combined concentration of calcium and magnesium, conventionally expressed as though it were all calcium carbonate. Forty milligrams per litre of calcium and ten of magnesium gives 141.1 mg/L as CaCO₃, which the USGS classifies as hard.
Magnesium punches above its weight in this calculation. Its conversion factor is 4.118 against 2.497 for calcium, because magnesium is lighter and so a given mass contains more moles. Ten milligrams of magnesium contributes 41.2 mg/L of hardness while forty of calcium contributes about 100.
The formula
Each ion concentration is multiplied by the ratio of the calcium carbonate molar mass to its own, giving the equivalent CaCO₃ concentration. Those are summed for total hardness. The conversion to grains per gallon, still used on water softener equipment, divides by 17.118.
| Term | Meaning |
|---|---|
| Hardness as CaCO₃ | The conventional unit, expressing all hardness ions as an equivalent calcium carbonate mass. |
| Grain per gallon | An older unit still used on softeners. One gpg is 17.118 mg/L. |
| Temporary hardness | The portion associated with bicarbonate, which precipitates on boiling as scale. |
| USGS classification | Soft below 60, moderately hard 60 to 120, hard 120 to 180, very hard above 180 mg/L. |
The inputs explained
| Field | What to enter |
|---|---|
| Calcium concentration [Ca²⁺] (mg/L) | Calcium concentration in mg/L, as the ion rather than as CaCO₃. |
| Magnesium concentration [Mg²⁺] (mg/L) | Magnesium concentration in mg/L, as the ion. |
When to use it
Sizing a water softener
Softener capacity is specified in grains, so hardness must be converted to that unit and multiplied by daily use.
Diagnosing scale problems
Scale in kettles, boilers and heat exchangers tracks hardness directly.
Interpreting a water report
Utility reports give calcium and magnesium separately, and this combines them into the standard figure.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How hard is water at each ion level?
A range of calcium concentrations against a fixed magnesium level.
| Calcium concentration | Water hardness | Hardness in grains per gallon | USGS classification |
|---|---|---|---|
| 10 mg/L | 66.2 mg/L as CaCO₃ | 3.86 | moderately hard |
| 40 mg/L | 141.1 mg/L as CaCO₃ | 8.24 | hard |
| 80 mg/L | 240.9 mg/L as CaCO₃ | 14.08 | very hard |
| 150 mg/L | 415.7 mg/L as CaCO₃ | 24.29 | very hard |
Questions
What is considered hard water?
The USGS classifies water above 120 mg/L as CaCO₃ as hard and above 180 as very hard. Below 60 is soft. The boundaries are conventions rather than health thresholds, since hardness is not a health concern at ordinary levels.
Why is hardness expressed as calcium carbonate?
It is a convention allowing different hardness ions to be added on a common basis. Calcium and magnesium contribute differently per milligram, so converting both to a CaCO₃ equivalent makes them additive. No actual calcium carbonate need be present.
What is the difference between temporary and permanent hardness?
Temporary hardness is associated with bicarbonate and precipitates as scale when heated, which is what furs a kettle. Permanent hardness is associated with sulfates and chlorides and does not. This calculator gives total hardness, the sum of both.
Is hard water bad for you?
No. Hardness is a nuisance rather than a health issue, causing scale and reducing soap lather. Some studies suggest a small cardiovascular benefit from harder water, though the evidence is not strong enough to act on. The practical concerns are appliances and plumbing.
For converting between concentration units, see the ppm to molarity calculator. For the underlying ion concentrations, see the molarity calculator.