The water hardness calculator above converts a hardness figure between every scale in common use and classifies the result. Hardness is reported as grains per gallon in the United States, as milligrams per litre of calcium carbonate almost everywhere else, in German degrees across central Europe, in French degrees in France and southern Europe, and occasionally in Clark degrees in older British documents. They all describe the same water, and the conversions between them are fixed multiples.
Arb Digital publishes free calculators that turn a number on a report into something you can act on. Here that means two things beyond the unit conversion: the classification band the water falls into, taken from the World Health Organization's background document on hardness, and the arithmetic connecting hardness to the amount of salt a softener consumes to remove it.
What This Water Hardness Calculator Does
Hardness is the total concentration of dissolved divalent metal ions in water, overwhelmingly calcium and magnesium. Because two different ions contribute, the convention is to express the total as though it were all calcium carbonate, which gives one comparable number regardless of the mix.
The tool works in two directions. If you have a laboratory report giving calcium and magnesium separately in milligrams per litre, it combines them into a calcium carbonate equivalent. If you have a single hardness figure in any of the seven units offered, it converts to all the others. Either way it reports the value on every scale, states the classification band, and shows where the water sits on that scale as a set of bars.
It also does the salt arithmetic. A softener works by ion exchange, swapping calcium and magnesium for sodium held on a resin bed, and periodically flushing the accumulated hardness away with brine. The amount of salt that consumes is proportional to the total grains of hardness removed, so daily water use multiplied by hardness in grains per gallon gives the load, and dividing by the salt efficiency of your own unit gives the weight of salt.
How to Use It
- Pick the mode. Calcium and magnesium if you have a full water analysis, total hardness if you have a single number from a test strip or a utility report.
- Enter the values. In ion mode, use the elemental concentrations — milligrams per litre of calcium, not of calcium carbonate.
- Choose the unit your total hardness figure is written in. Grains per gallon and milligrams per litre differ by a factor of about 17, which is the single most common conversion error.
- Set your daily water use in gallons if you want the salt figures. A rough household estimate is fine; the result scales linearly.
- Enter your softener's salt efficiency in grains per pound, taken from its own documentation rather than a generic figure.
The Formulas and How They Are Calculated
Everything is converted to milligrams per litre as calcium carbonate first. From calcium and magnesium, hardness = 2.497 × [Ca] + 4.118 × [Mg], both in mg/L. Those two coefficients are the ratio of calcium carbonate's molar mass, 100.09 g/mol, to the molar mass of each ion: 100.09 / 40.078 = 2.497 for calcium and 100.09 / 24.305 = 4.118 for magnesium. Magnesium counts for more per milligram simply because a magnesium atom is lighter, so a milligram of it is more ions.
The scale conversions are fixed. One grain per US gallon is 17.118 mg/L as CaCO3. One millimole per litre is 100.09 mg/L. One milliequivalent per litre is 50.04 mg/L, half the millimolar figure because the ions are divalent. One German degree is 10 mg/L of calcium oxide, which works out to 17.848 mg/L as CaCO3. One French degree is 10 mg/L as CaCO3 exactly. One Clark degree is one grain per Imperial gallon, which is 14.254 mg/L, and it differs from the American grain only because the Imperial gallon is larger.
Work the default. A supply with 80 mg/L of calcium and 25 mg/L of magnesium gives 2.497 × 80 = 199.8 plus 4.118 × 25 = 103.0, a total of 302.7 mg/L as calcium carbonate. That is 302.7 / 17.118 = 17.7 grains per gallon, 3.02 mmol/L, 17.0 German degrees, 30.3 French degrees and 21.2 Clark degrees. All six numbers describe the same water.
The Classification Bands, and What They Are Based On
The four-band classification used here is the one set out in the World Health Organization's background document on hardness in drinking-water: soft below 60 mg/L as calcium carbonate, moderately hard from 60 to 120, hard from 120 to 180, and very hard above 180. The same thresholds are used in United States geological reporting, which is why a figure quoted in one country is comparable with one from another.
Two things about those bands are worth understanding. They are descriptive rather than regulatory: there is no health-based drinking water guideline value for hardness. In the United States it appears among the secondary standards, which cover taste, odour and nuisance effects rather than safety, as set out in the EPA guidance on secondary drinking water standards.
The bands also compress at the top. Everything above 180 mg/L is "very hard", which covers water at 200 and water at 600 equally. That is why the bar display on this page keeps counting past the last threshold rather than simply filling: the practical difference between 200 and 600 is enormous for scaling and for softener sizing, even though the label is identical.
Grains, Degrees and Why So Many Scales Exist
The proliferation of units is historical rather than technical. The grain is an old apothecary mass unit, 1/7000 of a pound, and grains per gallon survives in the United States because domestic softeners are sized and sold in grains of capacity. The German degree was originally defined against calcium oxide because that was the form the analysis produced; the French degree was defined against calcium carbonate; the Clark degree was defined against the Imperial gallon. Each was a sensible local choice, and none of them was ever reconciled.
The practical result is a set of factors worth committing to memory if you deal with more than one. Roughly, one German degree is 1.79 French degrees, 1.25 Clark degrees and 1.04 grains per gallon. One grain per gallon is about 17 mg/L. That last one is the one that causes actual damage, because a softener rated at 30,000 grains and water quoted at 300 units can mean two very different things depending on which unit the 300 is.
There is one more distinction that unit conversion cannot resolve. Total hardness is the sum of all calcium and magnesium. Carbonate hardness, sometimes called temporary hardness, is the portion associated with bicarbonate, and it is the part that precipitates as scale when water is heated. Non-carbonate or permanent hardness is the remainder, associated with sulfate and chloride, and heating does not remove it. A single total-hardness number tells you nothing about the split, which is why a full analysis reports alkalinity alongside it.
What Hardness Actually Causes
The visible effects come from two different mechanisms. Scale forms because calcium bicarbonate decomposes on heating, depositing calcium carbonate on heat exchangers, kettle elements and pipe walls. This is why scaling appears in water heaters and boilers rather than in cold pipes, and why it tracks carbonate hardness specifically rather than total hardness.
Soap scum is a separate chemical reaction. Traditional soaps are sodium salts of fatty acids, and calcium displaces the sodium to form an insoluble calcium salt — the curd that leaves a ring on a bath. Modern synthetic detergents do not form insoluble calcium salts, which is why hard water affects bar soap far more visibly than it affects laundry detergent, though detergent formulations still include sequestrants to bind hardness ions.
Neither effect is a health matter, and hardness is not treated as a contaminant. Calcium and magnesium in drinking water are dietary minerals. The reason people soften water is scale, appliance life and the feel of it, not safety. What follows from that is that softening is an economic decision rather than a necessary one, and the salt figures on this page exist to let you put a number on the running cost side of it.
Reading a Water Report Without Double-Counting
The single most common error in this whole area is mixing bases. A laboratory report may quote calcium as 80 mg/L meaning elemental calcium, or as 200 mg/L meaning the calcium carbonate equivalent of that same calcium. Both are correct; they describe the same water; and feeding the second one into the elemental slot inflates the answer by a factor of two and a half.
The check is arithmetic. If a report lists calcium, magnesium and a total hardness figure, verify that 2.497 times the calcium plus 4.118 times the magnesium reproduces the stated total. If it does, the ion figures are elemental. If instead the calcium and magnesium simply add up to the total, they are already expressed as calcium carbonate and should go into total-hardness mode. That one test resolves the ambiguity every time.
Two smaller points. Test strips are semi-quantitative and typically resolve to the nearest 25 mg/L at best, so a strip reading is a band rather than a number. And hardness varies through the year in surface-water supplies and between wells drawing on different aquifers, so a single measurement describes one day. Our water usage calculator helps put a household figure on the daily volume this page needs, and the concentration converter handles unit rescaling on the other constituents of the same report.
Arb Digital publishes hundreds of free calculators across chemistry, maths, finance and marketing — no sign-up, no limits. If something you need is missing, tell us and we will look at building it.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Entering calcium already expressed as calcium carbonate into the elemental slot — it inflates the result by a factor of about 2.5. Check the report's basis first.
- Confusing grains per gallon with mg/L — they differ by about 17 times, and softener capacities are quoted in grains while laboratory reports are quoted in mg/L.
- Mixing American grains with Clark degrees — both are grains per gallon, but the Imperial gallon is larger, so the two scales differ by about twenty percent.
- Treating total hardness as carbonate hardness — only the carbonate portion precipitates as scale on heating, and total hardness alone does not tell you the split.
- Using a generic salt efficiency — the grains-per-pound figure depends on how a specific softener is programmed and varies by more than a factor of two.
Related Free Tools From Arb Digital
Estimate the daily volume this page needs with the water usage calculator, and put a number on a leak with the drip faucet calculator. For the chemistry side, rescale units on other constituents using the concentration converter, rewrite a strength across expressions with the solution concentration calculator, and get the molar masses behind the conversion factors from the molar mass calculator. The full free online tools hub lists everything else.
Frequently Asked Questions
It is the total concentration of dissolved divalent metal ions in water, in practice almost entirely calcium and magnesium. It is conventionally reported as though all of it were calcium carbonate, which gives one comparable figure regardless of the mix of ions.
Multiply by 17.118. One grain per US gallon is 17.118 milligrams per litre as calcium carbonate, and for fresh water milligrams per litre and parts per million are the same number.
The World Health Organization classification puts soft water below 60 milligrams per litre as calcium carbonate, moderately hard from 60 to 120, hard from 120 to 180, and very hard above 180. The same thresholds are used in United States geological reporting.
Multiply the calcium in milligrams per litre by 2.497 and the magnesium by 4.118, then add them. Those factors are the ratio of calcium carbonate's molar mass to each ion's, so 80 milligrams of calcium and 25 of magnesium give about 303 milligrams per litre.
One German degree is 10 milligrams per litre of calcium oxide, which converts to 17.848 milligrams per litre as calcium carbonate. A French degree is 10 milligrams per litre as calcium carbonate exactly, so the two scales differ by a factor of about 1.79.
Hardness is not treated as a health contaminant and there is no health-based guideline value for it. In the United States it falls under secondary standards, which address taste, appearance and nuisance effects such as scale and soap scum rather than safety.
Temporary or carbonate hardness is the portion associated with bicarbonate, and it precipitates as scale when the water is heated. Permanent or non-carbonate hardness is associated with sulfate and chloride and is not removed by heating. Total hardness alone does not reveal the split.
The load is daily gallons multiplied by hardness in grains per gallon, and the salt weight is that load divided by the softener's salt efficiency in grains per pound. That efficiency figure comes from the specific unit's documentation and varies widely with how it is programmed.
This calculator is provided for education and general reference. It converts between hardness scales and reports a published classification; it is not water treatment, plumbing, health or purchasing advice. Test results and equipment settings should be interpreted with your water supplier or a qualified professional.
