Number format · Procurement guide from the water-analysis desk · Published: October 2, 2026
Table of Contents
Key Takeaways
- Number one: 1 grain per gallon (gpg) = 17.1 mg/L of hardness as calcium carbonate. That is the anchor conversion for every US water report and softener capacity rating [1].
- Number two: 1 German degree (°dH) = 10 mg/L of calcium oxide = 17.848 mg/L as CaCO3, the unit on most European appliance and boiler specifications [2][3].
- Number three: 1 mmol/L = 100.09 mg/L as CaCO3, because the molar mass of CaCO3 is 100.09 g/mol — the unit of modern laboratory and standard-method reporting [3][6].
- Number four: 1 French degree (°f) = exactly 10 mg/L as CaCO3, the unit behind much Latin-American, French, and Spanish water documentation [5][6].
- The most expensive hardness conversion mistake is not the arithmetic but the chemistry. These units express a CaCO3 equivalent, which is not the mass of calcium actually dissolved in the water [3][6].
- Normalize every spec sheet to one unit before comparing bids. That one habit prevents the classic failures: an undersized softener, a double-dosed inhibitor, and a monitoring instrument ranged for the wrong concentration [1][4].
Why Four Units Still Survive
Water hardness is one concentration with four passports. Total hardness is the sum of the molar concentrations of calcium and magnesium ions, yet the industry reports it in parts per million (mg/L as CaCO3), grains per gallon, German degrees, French degrees, or millimoles per liter depending on which side of the Atlantic the equipment was designed [6]. The units exist because each regional industry standardized on a different reference — calcium oxide in Germany, an imperial grain in England, a US grain in America, a simple decimal fraction in France — and equipment documentation inherited them.
So conversion between ppm, gpg, and °dH is not optional pedantry. A US-built softener rated in grains, a European boiler manual demanding fewer than so many °dH, and a laboratory report in mmol/L may all describe the same water. Compare them without converting and you are comparing quantities that differ by factors of two to ten. Below, each of the four numbers that unlocks the conversion is defined, sourced, and mapped to where it is used.
Number 1 — 1 gpg = 17.1 mg/L as CaCO3
The grain per gallon is the native unit of the US water treatment trade. One grain is 64.79891 milligrams, and one US gallon is 3.7854 liters, so one grain of calcium carbonate dissolved in one gallon works out to 17.1 mg/L as CaCO3 — the conversion stated explicitly in state laboratory guidance, alongside the Water Quality Association classification scale, which runs from soft (below 1.0 gpg, below 17.1 mg/L) through very hard (10.5 gpg and above, 180 mg/L and above) [1].
Use this number whenever the document is American: softener grain capacities, resin ratings, most consumer water-quality reports. It is also the unit in which regeneration frequency math is naturally done, because grain capacity divided by hardness in gpg yields gallons of soft water. One more reason procurement should keep a gpg figure in the specification even when the project reports in mg/L.
Number 2 — 1 °dH = 10 mg CaO/L = 17.848 mg/L as CaCO3
The German degree, deutsche Härte, defines one degree as 10 milligrams of dissolved calcium oxide per liter of water [2]. Because calcium oxide and calcium carbonate differ in molar mass, the CaCO3-equivalent value of one °dH is 17.848 mg/L — the conversion given by European water-treatment references and repeated in appliance manuals. A washing machine set for 14 °dH, for example, corresponds to 250 mg/L as CaCO3, which classifies as very hard water [2][3][4].
Use this number for European equipment: boilers, dishwashers, dosing systems, and many industrial components whose hardness limits were written in Germany or Austria. The °dH scale is close to, but not identical with, gpg — one gpg is about 0.959 °dH — so the two must never be treated as interchangeable on a datasheet [6].
Number 3 — 1 mmol/L = 100.09 mg/L as CaCO3
The scientific unit expresses hardness as the molar concentration of divalent ions. One °dH corresponds to 0.17832 mmol/L of calcium and magnesium ions, and calcium carbonate has a molar mass of 100.09 g/mol, so one mmol/L of hardness equals 100.09 mg/L as CaCO3 [3]. Conversion tables for hard water show the same relationship at one decimal place: 1 mmol/L = 100.1 mg/L [6].
Use this number when the document is a standard method, a laboratory certificate, or a water-chemistry textbook — and increasingly in international tender documents, since mmol/L is the modern general-purpose unit in European norms. The practical trap sits exactly here: 100.09 mg/L is an amount-of-substance equivalent, not a mass of any real substance, because hardness is a sum of two different ions expressed as if it were all calcium carbonate [3][6].
Number 4 — 1 °f = 10 mg/L as CaCO3
The French degree, degré français, is the cleanest of the four. One degree is defined as 10 mg/L of calcium carbonate, equivalent to 10 ppm — no molar-mass gymnastics required [5]. Reference tables list 1 °fH as exactly 10 on the mg/L scale [6]. It follows that one °dH is about 1.785 °f, and one gpg is about 1.71 °f, which is why a French water report and a US report for the same sample differ by a factor of nearly two [6].
Use this number for documentation from France, Spain, and much of Latin America, and for membrane and dosing equipment specified with °f limits. One caution when reading it aloud or writing it: the lowercase f distinguishes the hardness degree from degrees Fahrenheit, and confusing the two in a specification has real procurement consequences [6].
The Four Numbers on One Page
| Unit | Equals (mg/L as CaCO3) | Where it is used | Conversion anchor |
|---|---|---|---|
| gpg (grain per gallon) | 17.1 | US water reports, softener grain capacities, WQA hardness classes [1] | 1 grain = 64.8 mg in 3.7854 L [1] |
| °dH (German degree) | 17.848 | European boilers, appliances, German-standard industrial equipment [2][3][4] | 1 °dH = 10 mg CaO/L [2] |
| mmol/L | 100.09 | Laboratory methods, European norms, international tenders [3][6] | Molar mass of CaCO3 = 100.09 g/mol [3] |
| °f (French degree) | 10.0 | France, Spain, Latin America, membrane/dosing specifications [5][6] | 1 °f = 10 mg CaCO3/L by definition [5] |
Two regional extras are worth pinning beside the table. The Clark degree (°Clark, English degree) — one grain per imperial gallon — equals 14.254 ppm as CaCO3, so any “English” hardness figure must not be run through the US-gpg conversion [5]. And the USGS classification scale in mg/L (soft 0–60, moderately hard 61–120, hard 121–180, very hard 181 and above) is a convenient neutral language for international meetings where nobody wants to convert units live [5].
The Traps That Cost Money
The first trap is equivalent versus actual. Every number in the table above is an “as CaCO3” equivalent — a common currency for two different ions — not the mass of calcium in the water. A hardness of 171 mg/L as CaCO3 is not 171 mg/L of calcium. Treat the equivalent as the ion concentration and you inflate the calcium figure, skewing everything downstream from dosing chemistry to scaling indices [3][6].
The second trap is unit look-alikes. °dH and °f differ by a factor of 1.785, gpg exists in US and imperial versions that differ by about 20 percent, and °f collides visually with Fahrenheit [5][6]. The third trap is capacity mismatch: softener capacity is rated in grains (a gpg-world unit) while feedwater is often reported in mg/L, so a specification written in one unit and verified in another without conversion produces a softener sized wrong by a factor of 17.1 — or more precisely, by whatever factor the author forgot. The defense is procedural, not mathematical: pick one unit for the project, convert every bid document into it, and require vendors to state units on every number.
One Language for the Bid Table
Hardness conversion is a small task with an outsized procurement payoff, because it is the difference between comparing equipment and comparing adjectives. Once the shortlist sits in one unit, the remaining differences — sensor quality, temperature handling, data integration, delivery — become visible. Shanghai ChiMay supports that exercise from the monitoring side: its in-line conductivity and multi-parameter analyzers report in the engineering units your specification uses, with documentation you can drop straight into a normalized bid table [7]. Normalize the units first; the right instrument choice usually follows within the hour.
References
- Wisconsin Department of Natural Resources — “pH, Alkalinity, Hardness” (laboratory certification basics, PDF). States 1 grain/gal = 17.1 ppm (mg/L) as CaCO3, shows the full derivation (64.79891 mg grain, 3.7854 L gallon), and reproduces the WQA hardness classification in gpg and mg/L. https://dnr.wisconsin.gov/sites/default/files/topic/LabCert/Basics_Gen_Chem_2002.pdf
- ALMAWATECH — “German hardness.” Defines 1 °dH = 10 mg CaO/L and gives the conversion 1 °dH = 17.848 mg CaCO3/L. https://www.almawatech.com/en/waste-water/water-hardness/
- Wikipedia — “dGH (Degree of General Hardness).” Defines 1 dGH as 10 mg CaO/L = 17.848 ppm CaCO3, gives the 0.17832 mmol/L equivalence, and states the molar mass of CaCO3 as 100.09 g/mol. https://en.wikipedia.org/wiki/DGH
- Water Hardness Scale — “What is °dH?” Defines the German degree as 10 mg CaO/L, converts 1 °dH = 17.848 mg/L (CaCO3), and works the 14 °dH ≈ 250 mg/L appliance example. https://www.waterhardnessscale.com/en/glossary/what-is-dh
- Hard water reference (Permanent hardness mirror) — Defines dGH as 10 mg/L CaO = 17.848 ppm, the Clark degree as 14.254 ppm, the French degree as 10 mg/L CaCO3, and reproduces the USGS mg/L classification. https://mediated.wiki/source/Permanent_hardness
- Wikiwand — “Hard water” (encyclopedic reference). Provides the full hardness unit conversion table (1 mmol/L = 100.1 mg/L; 1 dGH = 17.85; 1 gpg = 17.12; 1 °fH = 10) and notes the lowercase-f convention against Fahrenheit confusion. https://www.wikiwand.com/en/articles/Hard_water
- Shanghai ChiMay — Digital conductivity meter product overview, describing in-line conductivity instruments for water quality analysis with configurable measurement ranges and digital readouts. https://www.chimaycorp.com/tagdetail/2016386801239105536.html
About the author: Written by the Shanghai ChiMay Technical Editorial Team — engineers and application specialists focused on online water quality analysis and process instrumentation for industrial and municipal water systems.
