Water Total Hardness Calculator: Ca2+, Mg2+ → PPM, GPG

Total water hardness is a measure of the concentration of multivalent cations in water, calculated in terms of CaCO3 concentration.

For total water hardness calculation, we only use 2 cations: calcium ions (Ca2+) and magnesium ions (Mg2+). The total water hardness calculator takes into account both and expresses water hardness in terms of parts per million of CaCO3 (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:

  1. Calcium Ca2+ concentration.
  2. 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:

Total 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 Total Water Hardness (Explained)

Calculating total hardness of water 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:

  1. The concentration of calcium ions is 24 mg/L.
  2. 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.

2 thoughts on “Water Total Hardness Calculator: Ca2+, Mg2+ → PPM, GPG”

  1. Most water softeners I have looked at have a rating of 16,000, 32,000 or 64,000 grains. If my water test shows that we have 10 grains/gallon (very hard), how can I determine which softener I should use, and why?

    Reply
    • Hi Ken, you have to make the minimum water softener grain number calculation. Basically, you have two parameters that go into this equation; water hardness is grains/gallon (GPG) and weekly water usage in gallons. Here is the equation for how many grain water softener you need:

      Water Hardness (GPG) × Weekly Water Usage (Gallons) = Number Of Grains

      Example: You have a 10 GPG water hardness. Let’s say you use 2,000 gallons of water per weak. How many grain water softener do you need? Just put both numbers in the equation like this: 10 GPG × 2,000 Gallons = 20,000 Grains. In this case, you would go for 32,000 grain softener; 16,000 grain would be a bit too small.

      For all these calculations, you can use this simple water softener size calculator. Hope this helps.

      Reply

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