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Calcium & Magnesium to CaCO₃ Water Hardness

Estimate calcium-and-magnesium hardness as CaCO₃, classify the result, or recover one ion concentration from measured hardness and the other ion.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Calcium at 40 mg/L and magnesium at 10 mg/L give 141.06 mg/L CaCO₃-equivalent hardness, in the hard-water range.

H (mg/L as CaCO₃) = 2.497 × Ca (mg/L) + 4.118 × Mg (mg/L).

Worked example

Enter these known values and leave the other values blank.

Calcium concentration
40 mg/L
Magnesium concentration
10 mg/L
Ca + Mg hardness as CaCO₃
141.06 mg/L

Assumptions and limitations

  • The conventional rounded factors 2.497 and 4.118 express measured calcium and magnesium mass concentrations as calcium-carbonate-equivalent hardness. The result is not the concentration of dissolved CaCO₃ itself.
  • Use calcium and magnesium measurements from the same water sample and conditions. Other polyvalent ions may contribute to measured total hardness; this model includes only Ca and Mg.
  • All concentrations must be nonnegative. Enter any two independent quantities to solve the third; an inverse requiring a negative ion concentration is rejected. Zero calcium and magnesium give zero hardness.
  • The ppm selector assumes solution density of exactly 1 kg/L, making a mass ppm numerically equal to mg/L. For a different density, convert mass ppm to mg/L using that measured density before using a mass-per-volume selector. This tool has no density input.
  • Classifications use CaCO₃-equivalent mg/L regardless of display units: 0–60 soft, above 60–120 moderately hard, above 120–180 hard, and above 180 very hard. These continuous thresholds describe hardness, not drinking-water safety or permit compliance.
  • The US gallon and international pound conversions use exact definitions. They convert concentration units without changing the rounded chemical coefficients.

Common questions

Is hardness the sum of calcium and magnesium in mg/L?

No. Each ion concentration is multiplied by its CaCO₃-equivalent factor before adding the contributions.

When does one ppm equal one mg/L?

For mass ppm, the equality assumes solution density of 1 kg/L. A different density changes the mass-per-volume concentration.

Can hardness alone determine calcium and magnesium separately?

No. You also need one measured ion concentration to determine the other in this two-ion model.

References

Algebraically regroup captured inverses to subtract integer-coefficient concentration contributions before division, preserving exact zero-ion boundaries without clipping negative inferred concentrations. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference.

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