Larson–Skold Index

Also known as larson ratio · chloride sulfate ratio

\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}

sig figs

Worked example: Cl 50, SO4 80, Alk 150 mg/L → LS = 1.026. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Larson–Skold Index fits

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AlkTotal Alkalinity as CaCO₃ from Species · Alkalinity Remaining After Alum

In this toolkit

Scaling and corrosion indices6 formulas

Langelier Saturation Index from a Full Water Analysis: Larson-Skold asks whether the water attacks steel through its film. LSI asks whether the film can form at all. Read the two together.Ryznar Stability Index (RSI): The scaling side of the same water, weighted to say how hard it scales or corrodes rather than which way.Puckorius (Practical) Scaling Index: For poorly buffered water, where the measured pH misleads LSI and Ryznar.Corrosion Rate from Coupon Weight Loss: The index predicts pitting; a coupon measures what the water actually does to the metal.Cycles of Concentration from Chloride: Both use chloride as Cl⁻.Cooling Tower LSI at Cycles of Concentration: Both use total alkalinity as CaCO₃.

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Larson–Skold Index explained

Langelier and Ryznar only ever look at calcium carbonate. Larson and Skold, working on Great Lakes water for the Illinois State Water Survey in 1958, went after the other half of the story: chloride and sulphate are penetrating anions that break down the passive film on mild steel, while bicarbonate alkalinity helps repair it. Their index is a straight equivalents ratio: divide each ion by its equivalent weight (35.45 for Cl⁻, 48.03 for SO₄²⁻, 50.04 for alkalinity as CaCO₃) and compare aggressors to protectors. A water with 50 mg/L chloride, 80 mg/L sulphate and 150 mg/L alkalinity gives (1.410 + 1.666)/2.998 = 1.03.

Read it in thirds: below 0.8 chloride and sulphate are unlikely to interfere with film formation, 0.8 to 1.2 means corrosion rates run higher than open-recirculating norms, and above 1.2 you should expect localized pitting rather than general wastage. This is the index that explains why a softened, high-chloride makeup can hold a perfect +0.2 LSI and still perforate a carbon-steel line in eighteen months, and why blowing down a tower on conductivity alone concentrates exactly the ions Larson–Skold cares about. Note that it is silent on stainless and copper: for those, chloride's absolute concentration and temperature matter more than the ratio.

Larson–Skold Index formula

\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}

Where

$\mathrm{LS}$ = Larson–Skold Index
$\mathrm{Cl}$ = Chloride as Cl⁻ (mg/L)
$\mathrm{SO_4}$ = Sulphate as SO₄²⁻ (mg/L)
$\mathrm{Alk}$ = Total alkalinity as CaCO₃ (mg/L)

Where this comes from

Larson, T. E., & Skold, R. V. (1958). Laboratory studies relating mineral quality of water to corrosion of steel and cast iron. Corrosion, 14(6). Read it

In this toolkit

Scaling and corrosion indices

6 formulasLangelier, Ryznar, Puckorius, Larson–Skold and coupon corrosion rate — the indices that say whether water will scale or eat the pipe.

Revised 31 October 2026

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formula.expert. (2026, October 31). Larson–Skold Index Formula & Calculator. https://formula.expert/solvers/larson-skold-index

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