Five scales that look like different units of one thing, and are really one water described as three different compounds. Every factor here is a molar-mass ratio, not a constant someone measured.
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200 ppm
200.0 ppm as CaCO₃
Very hard on the USGS scale — Scale builds quickly; appliance life is measurably affected.
The same water on every scale
Hardness scales, and what each expresses the hardness as
Scale
Value
Expressed as
Note
ppm / mg/L as CaCO₃
200.0
CaCO₃
The international convention, and what a water utility usually publishes.
grains per US gallon
11.68
CaCO₃
US practice, and the unit every water softener is rated in. A grain is 1/7000 lb.
German degree (°dH)
11.21
CaO
Ten mg/L of calcium OXIDE — a different compound, which is where the 17.848 comes from.
French degree (°fH)
20.00
CaCO₃
Ten mg/L as calcium carbonate. The one scale that is a round multiple of ppm.
English / Clark degree (°e)
14.03
CaCO₃
Grains per IMPERIAL gallon. Same grain as gpg over a gallon 20% larger, so the numbers differ.
millimoles per litre
2.00
Ca²⁺ + Mg²⁺
The chemically honest unit — it counts the ions rather than a compound that is not there.
milliequivalents per litre
4.00
charge
Half a millimole, because both ions carry two charges. Common in ion-exchange work.
The “expressed as” column is the whole story. A German degree is ten milligrams of calcium oxide; a French degree is ten milligrams of calcium carbonate. Same water, different compound, so 1 °dH is 1.7848 °fH — and that number is the ratio of the two molar masses, 100.0869 over 56.0774, not a constant someone measured.
If your report gives calcium and magnesium instead
Total hardness298.6 ppm as CaCO₃17.44 gpg · 16.73 °dH
What each ion is worth as calcium carbonate
Ion
Molar mass
Factor
Your figure becomes
Calcium (Ca²⁺)
40.078 g/mol
× 2.497
199.8 ppm
Magnesium (Mg²⁺)
24.305 g/mol
× 4.118
98.83 ppm
A laboratory measures ions, not hardness. Reading “calcium 80 mg/L” as though it were a hardness figure understates the water by a factor of 2.50 — it is 200 ppm, not 80. And magnesium counts for more per milligram, not less, because it is the lighter atom.
Where 200.0 ppm sits
USGS hardness classification, in three scales
Class
ppm as CaCO₃
gpg
°dH
Soft
0–60
0.0–3.5
0.0–3.4
Moderately hard
60–120
3.5–7.0
3.4–6.7
Hard
120–180
7.0–10.5
6.7–10.1
Very hard
over 180
over 10.5
over 10.1
These are the US Geological Survey’s boundaries. They are a convention rather than a physical threshold, and other countries draw the lines elsewhere — German practice calls water hard from 14 °dH, which is 250 ppm and well above the USGS figure of 180. The same water can be “very hard” on one side of a border and merely “hard” on the other.
What a softener would have to remove
Hardness removed per day3,505 grains11.7 gpg × 300 gal
Days between regenerations6.8at 75% of the rated capacity
If the rating were achievable9.1the number the box quotes
A softener’s rated grain capacity is achieved only at a salt dose that is deliberately uneconomic; at a normal dose a resin bed delivers appreciably less, which is why the two figures above differ. Sizing against the rating rather than the usable capacity is the commonest mistake in softener selection — and the reason a unit that should regenerate weekly ends up doing it every five days.
Which hardness a figure means
Three different hardness figures, for three different questions
Figure
What it is for
Total hardness
All the calcium and magnesium. This is what a softener has to remove, and what a softener is sized on.
Carbonate (temporary) hardness
The part balanced by bicarbonate, which precipitates on heating. This is the part that scales a kettle, and the part boiling removes.
Permanent (non-carbonate) hardness
The remainder, balanced by sulphate and chloride. Boiling does not touch it; ion exchange does.
Everything on this page converts total hardness, which is what a softener is sized on and what a water report usually publishes. If the question is whether a kettle will scale, the relevant figure is the carbonate part — a water high in permanent hardness can be very hard and scale comparatively little. The two grain scales differ too: the imperial gallon is 1.201 times the US one, so the same grain spread over it is a lower concentration — a grain per US gallon is 1.201 English degrees. The same two-gallon problem turns up wherever grains and gallons meet.
What this converter covers
ppm, grains per gallon, German, French and English degrees, millimoles and milliequivalents — plus the ion figures a laboratory actually reports.
ppm, gpg, °dH, °fH, °e, mmol/L and meq/L, all derived from molar masses
Total hardness from a lab report’s calcium and magnesium
The USGS classification, converted into all three common scales
What a softener removes per day, and how often it regenerates
Total against carbonate and permanent hardness
Molar-mass derived Ppm is ambiguous Softener sizing US, UK, German, French
200 ppm is 11.7 gpg, 11.2 °dH and 20 °fH · calcium 80 mg/L is 200 ppm of hardness
The scales measure different compounds
Water hardness is reported in at least five scales, and the conversion factors between them look like arbitrary constants. They are not. Each scale expresses the same dissolved calcium and magnesium as a different chemical compound, and the factors are the ratios of those compounds’ molar masses.
What each scale actually says
Scale
Definition
Expressed as
In ppm
ppm / mg/L
Milligrams per litre
CaCO₃
1
°fH (French)
10 mg/L
CaCO₃
10
°e (English / Clark)
1 grain per imperial gallon
CaCO₃
14.254
gpg (US)
1 grain per US gallon
CaCO₃
17.118
°dH (German)
10 mg/L
CaO
17.848
Look at the last two rows. A French degree and a German degree are both “ten milligrams per litre”, and they differ by 78% — because the French one counts calcium carbonate and the German one counts calcium oxide. Divide 100.0869 by 56.0774 and you get 1.7848 exactly. The factor is chemistry, not convention.
The two grain scales differ for a different and equally concrete reason: they use the same grain over two different gallons. The imperial gallon is 4.54609 litres and the US gallon 3.785411784, so the same grain spread over the larger gallon is a lower concentration — one English degree is 0.833 grains per US gallon, and a grain per US gallon is 1.20095 English degrees. That is the same two-gallon problem that turns up in fuel economy and flow rate.
Once the pattern is visible the whole table stops needing to be memorised. Ask what compound, and over what volume — and the factor follows.
There is no chalk in the water
Hardness “as CaCO₃” describes a substance that is not present. The calcium in your water is dissolved as Ca²⁺ ions, along with magnesium as Mg²⁺, balanced by bicarbonate, sulphate and chloride. Calcium carbonate is what those ions would weigh if they were all combined with carbonate — a bookkeeping device, not a measurement.
The convention exists because it makes different waters comparable. Two supplies can have quite different mixtures of calcium and magnesium and behave almost identically in a kettle or a washing machine, because what matters is the total charge of divalent ions available to react with soap and to precipitate. Putting them on a common CaCO₃ basis makes those two waters the same number.
Knowing it is a convention resolves several confusions at once. It explains why magnesium counts for more per milligram than calcium — the magnesium atom is lighter, so a milligram of it is more moles. It explains why hardness has a millimole and a milliequivalent form, which are the chemically honest units and are what an ion-exchange calculation actually uses. And it explains why a hardness figure cannot be subtracted from a total-dissolved-solids figure: they are counting different things in different currencies.
It is also why “removing the calcium carbonate” is a slightly odd way to describe softening. A softener does not remove a compound; it exchanges the calcium and magnesium ions for sodium ones, leaving the water just as dissolved and no longer hard.
A lab report is not a hardness figure
This is the mistake that costs money. A water utility publishes hardness as CaCO₃. A laboratory analysis reports what it actually measured: calcium and magnesium, each in milligrams per litre of the ion itself. Those are different numbers for the same water, and reading one as the other understates the water by more than half.
Converting a lab report to hardness
Reported
Molar mass
Factor to CaCO₃
Example
Calcium (Ca²⁺)
40.078
× 2.497
80 mg/L → 200 ppm
Magnesium (Mg²⁺)
24.305
× 4.118
24 mg/L → 99 ppm
So a report showing 80 mg/L calcium and 24 mg/L magnesium is water of 299 ppm total hardness — very hard by any classification — even though neither number on the sheet looks alarming. Sizing a softener from the calcium figure alone would under-size it by a factor of 3.7.
The factor is just the molar-mass ratio, and it is bigger for magnesium precisely because magnesium is lighter. Both ions carry two charges, so one mole of either is one mole of hardness; the lighter atom simply packs more moles into a milligram. This is the same reasoning that makes the millimole the natural unit.
A practical tell: if a figure is labelled “Ca” or “calcium” rather than “hardness”, it needs converting. If it is labelled “hardness as CaCO₃”, it does not. If it is labelled neither, and the number is under about 150 for water that visibly scales, it is probably the calcium.
Total, carbonate and permanent
A third ambiguity, and one that matters for a different set of questions: the word “hardness” covers three figures.
Three hardness figures, three questions
Figure
What it counts
Answers
Total
All calcium and magnesium
How to size a softener
Carbonate (temporary)
The part balanced by bicarbonate
Whether a kettle will scale
Permanent (non-carbonate)
The rest — sulphate and chloride
What boiling will not fix
Carbonate hardness is called temporary because heating drives it out: bicarbonate decomposes, carbonate precipitates, and the scale ends up on the element. That is the white crust in a kettle, and it is why boiling genuinely softens some waters and not others.
Permanent hardness stays dissolved however hot the water gets. A supply that is high in sulphate can be very hard and scale comparatively little — the soap still refuses to lather, but the kettle stays clean. The reverse also happens: moderate total hardness that is almost all carbonate will scale enthusiastically.
Everything this converter does is total hardness, which is what utilities publish and what softeners are sized on. If the question is specifically about scaling, the figure to ask for is the carbonate part — often reported as “alkalinity” on a water analysis, in the same CaCO₃ currency.
What the number means in practice
The classification boundaries are a convention rather than a physical threshold, and different countries put them in different places. The USGS calls water hard from 120 mg/L and very hard from 180. German practice classifies in °dH and puts its hard boundary at 14 °dH, which is 250 mg/L — so the same water can cross a border and change category.
What actually changes with hardness is fairly narrow, and worth stating plainly because hardness attracts more claims than it deserves. Above roughly 120 mg/L soap consumption rises noticeably and scale becomes visible on taps and heating elements. Above roughly 200 the life of an unprotected water heater is measurably shorter, and the case for softening becomes economic rather than cosmetic. Below 60 the water is soft enough that soap is hard to rinse off, which some people dislike.
For softener sizing the arithmetic is simple: grains per gallon multiplied by gallons used per day gives grains removed per day, and a unit’s capacity divided by that gives the days between regenerations. The one thing worth being careful about is that a softener’s rated capacity is achieved only at a salt dose nobody actually runs, so sizing against the number on the box gives an interval about a third longer than reality. The calculator shows both figures for that reason.
Two things hardness does not tell you. It says nothing about whether water is safe to drink — that depends on parameters no hardness scale touches. And it says nothing about taste beyond the fact that very soft water is often described as flat, which is subjective and not what any of these numbers measure.
Related calculators
Other concentration and water tools:
Flow RateL/min, m³/h, GPM, CFM and barrels a day — with the two gallons, standard against actual CFM, and mass flow.
Densitykg/m³, lb/ft³, lb/in³ and lb/gal, with specific gravity against any water reference and the API scale that runs backwards.
Every conversion factor on this page is computed from the IUPAC standard atomic weights rather than transcribed from a chart, which is why 1 °dH appears as 17.848 rather than the rounded 17.9 that circulates. The classification boundaries are the USGS ones, and the method for turning measured calcium and magnesium into a hardness figure is the one in Standard Methods 2340 — the same document that defines the distinction between total, carbonate and non-carbonate hardness.
Hardness of Water — Water Science SchoolUnited States Geological Survey · verified 2026-09-07 · The soft / moderately hard / hard / very hard classification at 60, 120 and 180 mg/L as calcium carbonate, and the convention of expressing hardness as a CaCO₃ equivalent rather than as the ions actually present
Standard Methods 2340 — HardnessAmerican Public Health Association / AWWA / WEF · verified 2026-09-07 · The calculation of total hardness as CaCO₃ from measured calcium and magnesium — the molar-mass factors 2.497 and 4.118 — and the distinction between total, carbonate and non-carbonate hardness
Standard atomic weights of the elementsInternational Union of Pure and Applied Chemistry · verified 2026-09-07 · The molar masses every factor on this page is derived from — CaCO₃ 100.0869, CaO 56.0774, Ca 40.078 and Mg 24.305 — which is why 1 °dH is 17.848 ppm rather than a rounded 17.9
Conversion note
These are unit conversions and a rough sizing aid, not a water treatment design. Choosing and sizing a softener involves more than hardness and household size: the service flow rate the plumbing needs, iron and manganese that foul resin, the salt setting, whether a bypass is wanted for drinking water, and — in many places — local rules on discharging brine to a septic system or a sewer. The softener figures here use a nominal usable capacity of 75% of the rating, which is a common working assumption rather than a property of your unit; take the real capacity and salt dose from the manufacturer's own table. Water hardness varies through the year and between sources on the same supply, so a single reading is a snapshot. Nothing here says anything about whether water is safe to drink — hardness is a scaling and soap-consumption question, and drinking-water quality depends on parameters this page does not touch. For a supply that matters, use your utility's published analysis or a laboratory test on your own tap.
Published the Water Hardness Converter: ppm, grains per US gallon, German, French and English degrees, millimoles and milliequivalents per litre.
Derives every conversion factor from the IUPAC standard atomic weights rather than transcribing a chart, which is why one German degree appears as 17.848 ppm rather than the rounded 17.9 that circulates.
Establishes that the scales are not different units of one thing but the same water expressed as different compounds: a German degree is ten milligrams of calcium OXIDE while a French degree is ten milligrams of calcium CARBONATE, so the 1.7848 between them is the ratio of two molar masses.
Shows that the two grain scales use the same grain over two different gallons, so a grain per US gallon is 1.20095 English degrees -- the same two-gallon problem that appears in fuel economy and flow rate.
States plainly that there is no calcium carbonate in the water at all: hardness as CaCO3 is a bookkeeping convention for comparing waters with different calcium-to-magnesium mixtures, and the ions are dissolved rather than combined.
Explains the consequences of that convention -- why magnesium counts for MORE per milligram than calcium, why the millimole and milliequivalent forms are the chemically honest units, and why a softener exchanges ions rather than removing a compound.
Converts a laboratory report's calcium and magnesium into total hardness, the step that costs money when it is skipped: a sheet reading calcium 80 and magnesium 24 milligrams per litre is 299 ppm of hardness, and sizing from the calcium figure alone under-sizes by a factor of 3.7.
Separates total, carbonate and permanent hardness, noting that a softener is sized on total while whether a kettle scales depends on the carbonate part -- so a water high in permanent hardness can be very hard and scale comparatively little.
Gives the USGS classification converted into all three common scales, and notes that the boundaries are a convention rather than a threshold: German practice calls water hard from 14 degrees, which is 250 ppm against the USGS figure of 180.
Sizes a softener on grains removed per day, and reports the regeneration interval twice -- at a nominal 75 percent usable capacity and at the rated figure -- because a rated capacity is achieved only at a salt dose nobody runs.
States what hardness does not tell you: nothing about whether water is safe to drink, and nothing about taste beyond the subjective flatness of very soft water.
Verified by 59 automated cases, asserting each factor against its molar-mass derivation rather than a decimal, that the ion factors 2.497 and 4.118 are separately correct, and that the classification bands tile the line with no gap or overlap.
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