Langelier Saturation Index Calculator (LSI): CaCO3 Saturation (pH)

LSI or Langelier Saturation Index tells us if the CaCO3 in the water will precipitate, dissolve, or be in equilibrium. The LSI calculation is based on the saturation pH of CaCO3 (pHsat) and the actual pH of water (pHact). Here, we will help you out with all LSI calculations in a structured way (useful for pools, for example), using these 2 key tools:

  • Langelier Saturation Index Calculator. This is an online calculator, you don’t need Excel or anything else. You input 4 metrics from the water analysis (pH, TDS, Ca2+, alkalinity), and the calculator determines LSI automatically.
  • Langelier Saturation Index Formula. Admittedly, the LSI formula is a bit complex and ugly (we start with the simple LSI = pHact – pHsat formula). We will show you how you can use the Langelier index formula to calculate LSI (including examples).

Here is how we interpret the result from the LSI calculator:

  • If LSI is positive (LSI > 0), we have supersaturated water (limescale build-up water) and we will see CaCO3 (calcium carbonate) precipitation (forming unwanted scaling).
  • If LSI is equal to 0 (LSI = 0), the CaCO3 is in equilibrium (no precipitation, no dissolving).
  • If LSI is negative (LSI < 0), we have undersaturated water (corrosive water) that can dissolve additional CaCO3. This can lead to corrosion.

Quick Example: Pool water analysis tells us we have 8.5 pH water, with 250 mg/L TDS, 120 mg/L of calcium (as PPM of CaCO3), and 76 mg/L of alkalinity (as PPM of CaCO3). Using the calculator below, we can determine that LSI is 0.53. That means that the CaCO3 in the water will likely precipitate, and we will get limescale build-up (which we hate; we should use a water softener to remove excess CaCO3).

water analysis for lsi calculation
Water analysis for LSI calculation: Based on the calculated LSI, we can see if we need to add calcium (preventing corrosion), to remove calcium (preventing limescale build-up), or if the LSI is just right (we don’t have to do anything).

We see that for calculating LSI, we have to measure 4 distinct factors in our water analysis (actual pH, TDS, Ca2+ concentration, and alkalinity). Once you have these 4 numbers, you can use the following calculator to determine the LSI:

 

Note: We use the standard room temperature here (25°C, 77°F, or 298.15K).

Let’s look at 1 example just to illustrate how this online LSI calculator works:

Say the water analysis showed that the actual pH is 9, we have 300 mg/L TDS, 150 mg/L Ca2+ as CaCO3, and alkalinity is 90 mg/L as CaCO3. How to calculate LSI?

Simple. Just insert ‘9’ in the 1st pH field, ‘300’ in the 2nd TDS field, ‘150’ in the 3rd Ca concentration field, and ’90’ in the 4th alkalinity field, and we get this result (screenshot):

lsi calculator determining langelier saturation index and caco3 saturation

We can see that at these water analysis results, we have a 1.19 LSI. Since LSI is above 0, that means that water is supersaturated with CaCO3, and we can expect CaCO3 precipitation (limescale buildup); the last line in the calculator tells you this as well.

Now, let’s have a look at the formula under the hood of this LSI calculator:

Langelier Index Formula (LSI Formula)

The formula for calculation LSI seems simple at first, but it’s actually quite a complicated equation when you put it to real use. Here is the basic LSI formula:

LSI = pHact – pHsat

Basically, in order to calculate LSI, we just have to subtract CaCO3 saturation pH from the actual (measured) pH. Sounds simple, right? Well, the complexity comes along when we want to express saturated pH. Here is the formula for calculating at which pH the CaCO3 is saturated:

pHsat = 9.3 + A + B – C – D

Every one of these letters (A, B, C, D) is a separate equation:

  • A = (log10(TDS) – 1) / 10. To calculate A, we need to measure TDS in mg/L or PPM (these are quantitatively the same unit. Example: 20 mg/L = 20 PPM).
  • B = -13.12 × log10(T(°C) + 273.15) + 34.55. This factor B takes into account the temperature (LSI depends on temperature as well). We usually take the standard room temperature (25°C or 77°F).
  • C = log10(Ca2+ as CaCO3) – 0.4. This ‘Ca2+ as CaCO3′ is also referred to as calcium hardness. It is calculated by multiplying Ca2+ concentration by 2.5 factor.
  • D = log10(alkalinity as CaCO3). This is why we have to measure alkalinity (as CaCO3) in water analysis to determine the LSI adequately.

Now, if we input all of these A, B, C, D equations into the LSI equation, we get this dreadful and complex equation:

LSI = pHact – 9.3 – (log10(TDS) – 1) / 10 + 13.12 × log10(T(°C) + 273.15) + 34.55 + log10(Ca2+ as CaCO3) – 0.4 + log10(alkalinity as CaCO3)

You have to admit this LSI formula is quite hard to calculate using a hand calculator. That’s why using the LSI calculator above is so much easier. But let’s just solve one example with this gigantic equation (just for fun).

Example: What is the LSI factor at 7.2 pH, 200 mg/L TDS, 90 mg/L calcium ions as CaCO3, and 33 mg/L alkalinity (as CaCO3), and 25°C (77°C)? Let’s input all these numbers in that long LSI equation like this (with the result):

LSI = 7.2 pH – 9.3 – (log10(200 mg/l TDS) – 1) / 10 + 13.12 × log10(25°C + 273.15) + 34.55 + log10(90 mg/L) – 0.4 + log10(33 mg/L) = -1.25 LSI

We can see that get a negative LSI (-1.25 LSI, to be specific). This means that the water is undersaturated with CaCO3 and that we can dissolve additional CaCO3 in it. Usually, this means that we should expect corrosion in the pipes.

Let’s have a closer look at the interpretation of the LSI result:

Practical Interpretation Of LSI

Alright, let’s say that you have a pool. You do the water analysis and use the LSI calculator above to determine the Langelier Saturation Index. It’s just a number, right? Let’s have a look at what this LSI number actually tells you (+ actionable actions you can take).

Theoretically, positive LSI means you will have limescale build-up, and negative LSI means you will have corrosion in your pool. You want to get LSI to 0 (equilibrium); at LSI = 0, you will not have limescale build-up or corrosion.

This is the theory. In practice, nobody really has a pool water with exactly 0 LSI. What we really aim for (especially with pools) is to get the LSI between -0.50 LSI and +0.50 LSI.

Example: If you calculate your pool water has 0.34 LSI, you don’t really need to worry or do anything. Theoretically, you will get limescale build-up, but practically this is a very tolerable build-up (you will probably not even notice it).

You do have to panic (a bit) if the calculated LSI is above +0.50 (say 1.31 LSI) or below -0.50 (say -0.97 LSI). This means you will have a high risk for limescale build-up and corrosion, respectively.

Here are the actionable things you can do if your pool has LSI outside of the safe -0.50 to +0.50 LSI range:

  • If LSI is below -0.50, you should add calcium (to avoid corrosion). We usually use calcium chloride (CaCl2) or cheaper calcium carbonate (CaCO3) to increase LSI (just be careful you don’t pour too much of it in your pool; you don’t want the LSI to surpass +0.50).
    adding caco3 to increase pool water langelier saturation index
    This is how powdered CaCO3 (calcium carbonate) looks like.
  • If LSI is above +0.50, you should do something to remove calcium ions from your pool water (to avoid limescale build-up). This is usually referred to as ‘water softening’. We usually use pool flocculant; this is a chemical that induces calcium agglomeration (practically limescale). You then remove these calcium crystals by vacuuming the pool, using the sand filter to remove clumps, etc. The other way is to empty the pool, and fill it with softer water (you will need a big water softener to soften your water).

We hope this makes clear what the Langelier Saturation Index is and how to use it to avoid limescale/corrosion. You can read further about the LSI Index here.

The LSI calculator and example above can help you to calculate LSI yourself. If, however, you need a bit of our help, you can use the comment section below, give us numbers from your water analysis, and we can do some math together.

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