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Calculating Hardness from Calcium and Magnesium Concentrations

Published in Water Hardness Calculation 3 mins read

How to Calculate Water Hardness?

Water hardness is typically calculated based on the concentrations of calcium (Ca) and magnesium (Mg) ions present. These ions are primarily responsible for water hardness. The calculation is expressed in milligrams per liter (mg/L) or grains per gallon (gpg), as calcium carbonate (CaCO₃).

Several methods exist for determining water hardness, including:

The most common method utilizes the following formula:

Hardness (mg/L as CaCO₃) = 2.497 [Ca] + 4.118 [Mg]

Where:

  • [Ca] represents the concentration of calcium ions in mg/L.
  • [Mg] represents the concentration of magnesium ions in mg/L.

This formula highlights that magnesium ions contribute more significantly to hardness than calcium ions, due to the differing molar masses and the way hardness is expressed.

Example:

If your water sample contains 20 mg/L of calcium and 10 mg/L of magnesium, the hardness would be:

Hardness = 2.497 20 + 4.118 10 = 89.96 mg/L as CaCO₃

This result indicates a water hardness of approximately 90 mg/L as CaCO₃.

Estimating Hardness from Total Dissolved Solids (TDS)

For a rough estimation, you can use the following approximation:

Hardness (mg/L as CaCO₃) ≈ TDS (ppm) / 10

Where TDS is the total dissolved solids measured in parts per million (ppm). Keep in mind that this is an estimate and not as precise as the calculation using calcium and magnesium concentrations. It assumes a significant portion of the TDS comes from hardness-causing minerals.

Using a Water Hardness Calculator

Many online calculators are available to simplify this calculation. These calculators typically require you to input the calcium and magnesium concentrations (or other relevant mineral content) to obtain the water hardness value. Examples include:

These tools provide a convenient way to determine water hardness without manual calculations.

Important Considerations

  • Units: Always ensure consistent units throughout your calculations (mg/L, ppm, gpg).
  • Accuracy: The accuracy of the calculated hardness depends heavily on the accuracy of the initial measurements of calcium and magnesium concentrations. Professional water testing is recommended for precise results.
  • Types of Hardness: The calculations above typically focus on permanent hardness. Temporary hardness, caused by bicarbonates, requires different calculation methods.

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