Water hardness is a measure of the concentration of multivalent cations in water, calculated in terms of CaCO3 concentration.
This primarily means calcium ions (Ca2+) and magnesium ions (Mg2+). Water hardness calculator takes into account both and expresses water hardness in terms of parts per million (ppm) and GPG (grains per gallon).
Any water source that has more than 60 ppm is considered a hard water source.
Example: Well water is hard because it contains 60+ ppm of Ca2+ and Mg2+. Rainwater is soft because it contains less than 60 ppm of these cations.
Calculating the hardness of water requires two parameters, namely:
- Calcium Ca2+ concentration.
- Magnesium Mg2+ concentration.
Water hardness is then simply calculated as:
Calcium Ca2+ conc. + Magnesium Mg2+ conc. = Total Water Hardness
Using this equation, we have designed a water hardness calculator that can calculate the total hardness of your water:
Water Hardness Calculator
You can freely use this calculator; by inputting calcium and magnesium hardness, you will get the total water hardness in ppm. If you get more than 60 ppm, that means you have hard water and should look into investing in a water softener system.
If you are looking to get grains per gallon (gpg; also a valid unit for water hardness), you can convert ppm to gpg here.
How Do You Calculate The Water Hardness (Explained)
Calculating hardness takes into account the dissolution of all elements that contain calcium and magnesium atoms. The base equation we use to measure total hardness is the dissolution of calcium carbonate:
CaCO3 + CO2 + H2O ⇌ Ca2+ + 2 HCO3–
All calcium and magnesium ions are expressed as an equivalent of calcium carbonate (CaCO3). To calculate the total water hardness, we have to transform all hard water ions into the hypothetical concentration of calcium, we need molar masses of:
- Molar mass (M) of CaCO3= 101 g/mol
- M Ca2+ = 40,1 g/mol
- M Mg2+ = 24,3 g/mol
Now, we calculate the ratio of molar masses with respect to MCaCO3:
MCaCO3/MCa = 100,1 / 40,1 = 2,5
MCaCO3/MMg = 100,1 / 24,3 = 4,1
Now we can express all calcium and magnesium two-valent cations into calcium carbonate concentration like this:
[CaCO3] = 2.5 * [Ca2+] + 4.1 * [Mg2+]
The resulting hardness is expressed in units mg/l of CaCO3; that are equal to ppm.
Chemically, all this might be a bit complex. Let’s simplify the water hardness calculation by an example.
Calculating Hardness Example
Let’s say that we have two known parameters:
- The concentration of calcium ions is 24 mg/L.
- The concentration of magnesium ions is 28 mg/L.
We can use the following equation to calculate the total hardness of water:
Total Water Hardness =[CaCO3] = 2.5 * [Ca2+] + 4.1 * [Mg2+]
Let’s input both concentrations like so:
Total Water Hardness =[CaCO3] = 2.5 * 24 mg/L + 4.1 * 28 mg/L = 174.80 mg/L
The result is the total hardness of water: 174.80 mg/L or 174.80 ppm. If you have such a high water hardness, you might want to consider using a salt-free water softener to reduce the water hardness below 60 ppm.
If you have any questions about the water hardness calculator, you can pose them in the comments below.