Water hardness and softening

grains per gallonhardness as CaCO3GPGsoftener sizingsalt doseresin capacity

Hardness as CaCO₃, grains per gallon, resin volume, salt dose and days between regenerations — sizing and running a softener.

Total Hardness as CaCO₃

TH=2.497Ca+4.118Mg\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}

Converts a lab report's calcium and magnesium ion results into a single total hardness expressed as milligrams per litre of CaCO₃.

Grains per Gallon ↔ ppm Hardness

H=17.118GH = 17.118\,G

Converts water hardness between grains per US gallon and mg/L as CaCO₃ using the exact 17.118 mg/L per grain trade factor.

Ion Concentration as CaCO₃ Equivalent

CCaCO3=Cion×50.04EWC_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \frac{50.04}{\mathrm{EW}}

Restates any ion's concentration in the trade's common currency of CaCO₃ by scaling with the ratio of equivalent weights, 50.04 over the ion's own.

Equivalent Weight from Molar Mass and Valence

EW=Mz\mathrm{EW} = \frac{M}{z}

Gives the gram-equivalent weight of an ion or compound as its molar mass divided by the number of charges or replaceable hydrogens it carries.

Hardness Load Removed per Regeneration

m=CVm = C \, V

Gives the mass of hardness as CaCO₃ a softener must remove between regenerations from the raw hardness and the volume of water treated.

Softener Resin Volume Required

V=mcapqV = \frac{m_{\text{cap}}}{q}

Sizes the ion-exchange resin bed from the hardness capacity required per regeneration and the resin's rated capacity per unit volume.

Salt Dose per Regeneration

msalt=DVm_{\text{salt}} = D \, V

Gives the mass of sodium chloride a softener draws each regeneration from the resin volume and the programmed salt dosage per unit volume.

Days Between Softener Regenerations

t=mcapCQt = \frac{m_{\text{cap}}}{C \, Q}

Gives the run time a softener achieves between regenerations from its rated hardness capacity, the raw water hardness and the average water usage rate.

How they fit together

Hardness is calcium and magnesium, but they have different molar masses, so the trade converts everything to an equivalent weight of calcium carbonate and adds the numbers. That is what "as CaCO₃" means on every water report, and it is why 1 grain per gallon = 17.1 mg/L as CaCO₃ — one grain, 64.8 mg, in one US gallon, 3.785 L. Sizing follows from there: hardness times water used gives grains removed, which against the resin's capacity gives the volume of resin and the interval between regenerations.

The choice that matters is salt dose, because resin capacity is not a constant — it is bought. At 6 lb of salt per cubic foot you get roughly 20,000 grains per ft³, about 3,300 grains per pound of salt, which is efficient. Push to 15 lb/ft³ and capacity rises to about 30,000 grains but efficiency falls to near 2,000 grains per pound, so you are buying the last third of the capacity at twice the price and sending the difference to the drain. High-salt settings are for when leakage must be low; efficiency settings are for volume. Two field errors: quoting hardness in mg/L as Ca rather than as CaCO₃, which understates it by a factor of 2.5, and sizing off nameplate capacity while ignoring that iron, low temperature and high flow rate all cut real throughput well below the catalogue number.