Water Hardness Calculator - ppm, German & French Degrees
Calculate water hardness from calcium and magnesium concentrations. Get ppm CaCO3, German degrees, and French degrees, with a soft to very hard classification.
Water Hardness Calculator
Input Parameters
Calculation Formula:
Hardness = (Ca²⁺ × 2.5) + (Mg²⁺ × 4.1) + Other Minerals
Results
Documentation
Water Hardness Calculator
A water hardness calculator turns the calcium and magnesium content of a water sample into a single hardness value. It reports the result in parts per million (ppm) of calcium carbonate, in German degrees (°dH), and in French degrees (°f), and it classifies the water as soft, moderately hard, hard, or very hard.
What is water hardness?
Water hardness is a measure of dissolved minerals in water, mainly calcium (Ca²⁺) and magnesium (Mg²⁺) ions. These minerals dissolve into water as it moves through soil and rock, especially limestone and chalk. Water with a lot of dissolved calcium and magnesium is called "hard." Water with little of these minerals is called "soft."
Hardness does not usually make water unsafe to drink. It does affect how well soap lathers and how much scale builds up in pipes, kettles, and water heaters.
How to calculate water hardness
Total water hardness is expressed in ppm of calcium carbonate (CaCO₃), even though the hardness actually comes from several different minerals. The formula used here is:
Total Hardness (ppm CaCO₃) = (Ca²⁺ × 2.5) + (Mg²⁺ × 4.1) + Other Minerals
- Ca²⁺ is the calcium concentration, in ppm.
- Mg²⁺ is the magnesium concentration, in ppm.
- Other Minerals is the combined concentration of any additional hardness-causing minerals, in ppm.
The multipliers, 2.5 for calcium and 4.1 for magnesium, convert each ion's concentration into its calcium-carbonate-equivalent weight.
Converting to other hardness units
Once the total is known in ppm CaCO₃, it can be converted to two other common scales:
| Unit | Conversion from ppm CaCO₃ |
|---|---|
| German degrees (°dH) | ppm ÷ 17.848 |
| French degrees (°f) | ppm ÷ 10 |
Parts per million and milligrams per liter (mg/L) of CaCO₃ are the same number for water and are the standard unit in the United States. German degrees are common in Germany and central Europe. French degrees are common in France and several other European countries.
Water hardness classification
Once the total hardness in ppm is known, it falls into one of four standard classes:
| Classification | ppm CaCO₃ | German degrees (°dH) | French degrees (°f) |
|---|---|---|---|
| Soft | 0–60 | 0–3.4 | 0–6 |
| Moderately hard | 61–120 | 3.4–6.7 | 6.1–12 |
| Hard | 121–180 | 6.8–10.1 | 12.1–18 |
| Very hard | above 180 | above 10.1 | above 18 |
Worked example
Suppose a water sample has a calcium concentration of 40 ppm, a magnesium concentration of 10 ppm, and 5 ppm of other hardness minerals.
- Calcium contribution: 40 × 2.5 = 100 ppm CaCO₃
- Magnesium contribution: 10 × 4.1 = 41 ppm CaCO₃
- Add the other minerals: 100 + 41 + 5 = 146 ppm CaCO₃
The total hardness is 146 ppm CaCO₃. Converted to German degrees, that is 146 ÷ 17.848 ≈ 8.2 °dH. Converted to French degrees, it is 146 ÷ 10 = 14.6 °f. Because 146 falls between 121 and 180 ppm, the water is classified as hard.
How to use the calculator
- Enter the calcium concentration (Ca²⁺) in ppm. This figure is usually available on a water quality report or a home test kit.
- Enter the magnesium concentration (Mg²⁺) in ppm.
- Enter the concentration of other hardness minerals in ppm, if known. This field is optional.
- Read the results: total hardness in ppm CaCO₃, the German- and French-degree equivalents, and the hardness classification.
- Use the "Copy Results" button to copy the figures for a report or a message.
Where to find mineral concentration data
- Water quality report. Most municipal water suppliers publish an annual report, sometimes called a Consumer Confidence Report, listing mineral levels.
- Home test kit. Inexpensive kits measure calcium and magnesium directly, usually with test strips or a titration test.
- Professional testing. Water treatment companies and some local health departments offer lab testing.
- Well water. Because well water is not covered by a municipal report, private wells should be tested directly, ideally once a year.
Effects of water hardness
Soft water (0–60 ppm) lathers soap easily and leaves little scale. It can taste flat to some people and, in older buildings with metal pipes, may be more likely to pick up trace metals from the plumbing.
Moderately hard water (61–120 ppm) is a middle ground. It carries some dissolved minerals but rarely causes noticeable scale or cleaning problems.
Hard water (121–180 ppm) leaves visible scale on fixtures, appliances, and glassware. It needs more soap or detergent to produce a lather and can shorten the working life of water heaters.
Very hard water (above 180 ppm) causes heavy scale buildup, sharply reduces soap efficiency, and can give water a noticeable taste. Homes with very hard water commonly install a water softener.
Temporary and permanent hardness
Hardness is sometimes split into two types by cause. Temporary hardness comes from calcium and magnesium bicarbonates. Boiling the water drives off carbon dioxide and causes these bicarbonates to form solid carbonate scale, which is why kettles crust over with use. Permanent hardness comes from calcium and magnesium sulfates, chlorides, and nitrates, and boiling does not remove it. It usually requires a water softener or another chemical treatment. A hardness calculator reports the total of both types together.
Reducing water hardness
- Ion exchange softener. The most common home solution. It swaps calcium and magnesium ions for sodium or potassium ions and needs periodic refilling with salt.
- Template-assisted crystallization (TAC). A salt-free system that turns dissolved minerals into tiny crystals that stay suspended in the water instead of forming scale on surfaces.
- Reverse osmosis. Removes most dissolved minerals, including hardness minerals, by forcing water through a fine membrane. It uses more water than it produces as usable output.
- Chemical precipitation. Used mainly in industrial settings to make hardness minerals settle out of solution.
Frequently asked questions
What causes water hardness? Dissolved calcium and magnesium ions cause water hardness. They enter groundwater as it passes through rock and soil containing limestone, chalk, or gypsum.
Is hard water safe to drink? Yes. Hard water is not a health hazard, and the calcium and magnesium in it add small amounts of dietary minerals. Very hard water can have an unpleasant taste to some people.
Does hard water damage plumbing and appliances? Over time, yes. Scale builds up inside pipes, water heaters, and coffee makers, which reduces efficiency and can shorten their lifespan.
What is the difference between water hardness and TDS? Total dissolved solids (TDS) measures every dissolved substance in water, including sodium, chloride, and sulfate. Water hardness measures only calcium and magnesium. Water can have high TDS with low hardness if most of its dissolved content is something other than calcium or magnesium.
How often should water be tested for hardness? Municipal water is usually fine to check once a year using the supplier's water quality report. Well water should be tested every six to twelve months, since groundwater conditions can change with the season.
Can this calculator be used for aquarium water? Yes. Many fish and plant species need a specific hardness range, so calculating the ppm or degree value of aquarium water helps match it to those requirements.
References
- World Health Organization. Hardness in Drinking-water, 2011.
- United States Geological Survey. Water Hardness, Water Science School, 2019.
- American Water Works Association. Water Quality & Treatment: A Handbook on Drinking Water, 6th ed., 2014.