Langelier Saturation Index (LSI) Calculator

Understanding the Langelier saturation index calculator — concept and principle

The Langelier Saturation Index (LSI) tells you whether water tends to deposit calcium carbonate scale or to dissolve it, by comparing its actual pH with the pH at which it would be exactly saturated with calcium carbonate (pHs). Pool operators, cooling-tower technicians and water utilities use it to keep pipes and surfaces neither scaled nor corroded.

Water above its saturation pH lays down scale; below it, water dissolves scale and metal.

How it is calculated

pHs = (9.3 + A + B) − (C + D)
A = (log₁₀ TDS − 1) ÷ 10, with total dissolved solids in mg/L.
B = −13.12 × log₁₀(T + 273.15) + 34.55, with T in °C converted to kelvin.
C = log₁₀(calcium hardness) − 0.4, hardness in mg/L as CaCO₃.
D = log₁₀(total alkalinity), in mg/L as CaCO₃.
LSI = pH − pHs, and the Ryznar index RSI = 2 × pHs − pH.

More calcium, alkalinity or heat lowers pHs (more scaling); more dissolved salts raise it slightly.

The principle

Calcium carbonate solubility depends on calcium and carbonate ions, temperature and ionic strength, and carbonate in turn depends on pH and alkalinity. Langelier (1936) combined the solubility product with the carbonic-acid equilibrium to find the one pH at which water is in balance with solid CaCO₃. Above pHs the water is supersaturated and tends to deposit scale; below it, the water is undersaturated and can dissolve protective carbonate layers. The A–D terms are an empirical fit to those constants for natural waters.

Worked example

Inputs: pH 7.8, T = 25 °C, TDS = 300 mg/L, calcium hardness 150 mg/L, alkalinity 120 mg/L.
A = (log 300 − 1) ÷ 10 = 0.1477; B = −13.12 × log 298.15 + 34.55 = 2.0854.
C = log 150 − 0.4 = 1.7761; D = log 120 = 2.0792.
pHs = (9.3 + 0.1477 + 2.0854) − (1.7761 + 2.0792) = 7.6779.
LSI = 7.8 − 7.6779 = 0.122, within ±0.3, so balanced.
RSI = 2 × 7.6779 − 7.8 = 7.556.

Each point is the calculator re-run with only “pH” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

pH	LSI
1.95	-5.727854865
3.9	-3.777854865
5.85	-1.827854865
7.8	0.1221451351
9.75	2.072145135
11.7	4.022145135
15.6	7.922145135

How to read the result

Where does your result fall?

An LSI above +0.3 indicates a scaling tendency, −0.3 to +0.3 is near equilibrium (the band used here), and below −0.3 the water is aggressive. For the Ryznar index, below about 6 suggests scaling, 6–7 roughly stable and above 7 increasingly corrosive. The two can disagree, as in the example, so treat them as indicators rather than a verdict.

Common mistakes

Entering calcium as mg/L Ca instead of mg/L as CaCO₃ (multiply Ca by about 2.5 to convert).
Using total hardness instead of calcium hardness.
Measuring pH at one temperature and calculating at another.

Keep in mind: The LSI only describes the calcium carbonate driving force, not corrosion from oxygen, chloride or microbes, nor how fast scale forms. Treatment of boilers, cooling systems or public supplies should follow local standards and a qualified water specialist.

Frequently asked questions

How do I raise or lower the LSI?

Raise or lower pH, alkalinity or calcium hardness. pH has the most direct effect.

Why does hot water scale more?

Calcium carbonate is less soluble at higher temperature, so pHs falls and the LSI rises. That is why kettles, heaters and heat exchangers scale first.

Sources: W. F. Langelier, "The analytical control of anti-corrosion water treatment," Journal AWWA 28(10), 1936 · APHA/AWWA/WEF, Standard Methods for the Examination of Water and Wastewater, Method 2330 (Calcium Carbonate Saturation)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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