Water Hardness Calculator
Grains, German degrees and ppm all measure the same calcium — as milligrams of chalk per litre.
The formula
mg/L as CaCO3 = value * unit factor ; TDS = EC * 0.65
One substance, five scales
Hardness is reported as though every dissolved calcium and magnesium ion were calcium carbonate, which gives a single number that different regions then divide by different constants. A grain per US gallon is 17.1 mg/L, a German degree 17.8, a French degree exactly 10. The underlying water is unchanged; only the arithmetic in front of it differs.
Hardness is not dissolved solids
A conductivity meter counts every ion in the water and multiplies by a factor between about 0.5 and 0.8 to report total dissolved solids. Hardness counts only calcium and magnesium. Softened water keeps almost all of its conductivity, because ion exchange swaps calcium for sodium rather than removing anything — the water is soft and the dissolved solids are barely touched.
Which denominator?
Most of the confusion in solution work is not arithmetic but bookkeeping. Molarity divides by the volume of the finished solution; molality divides by the mass of the solvent; percent by mass divides by the mass of the solution again. The three agree closely in dilute water and diverge sharply in concentrated acid, which is why a bottle labelled 98 % is also labelled 18.4 M without contradiction.