The Langelier saturation index (LSI) is measured pH minus the pH at which water is saturated with calcium carbonate (pHs): a positive LSI marks water that tends to deposit CaCO3 scale, a negative LSI water that tends to dissolve it. The LSI needs 5 inputs (pH, calcium hardness, alkalinity, TDS and temperature), so how is pHs calculated, and how far can the result be trusted?
Six related indices, from Ryznar (RSI) and Puckorius (PSI) to the CCPP, fill its gaps, and together they decide how hard the scale inhibitors, acids and alkalis among water treatment chemicals have to work.
Three worked examples give LSI +1.29 for a cooling tower, -1.05 for a soft municipal water and +1.46 for an RO concentrate; every source treats the LSI as directional, not quantitative.
Every formula, factor and limit on this page is checked against primary sources (Veolia Water Technologies Handbook, UFC 3-240-13FN, ASTM, DuPont FilmTec manual, peer-reviewed reviews); see our methodology and fact-checking process.
What Is the Langelier Saturation Index (LSI)?#
The Langelier saturation index is the difference between the measured pH of a water and its saturation pH (pHs), the pH at which that water is exactly saturated with calcium carbonate. pHs is a calculated value that falls as calcium, alkalinity and temperature rise. W.F. Langelier published it in the Journal of the American Water Works Association in 1936 (28(10):1500-1521). Veolia's Water Technologies Handbook (chapter 25) treats it as a directional tendency for pH 6.5 to 9.5, not a quantity of scale.
What does a positive, zero or negative LSI mean?#
A positive LSI means the water is supersaturated with calcium carbonate and tends to deposit scale, a negative LSI means it is undersaturated and tends to dissolve CaCO3, and zero means saturation. The aqion convention treats ±0.03 as equilibrium. Carrier and Hach Method 8073 classify LSI values as follows.
| LSI | Carrier classification (as reproduced by Lenntech) | Hach Method 8073 class |
|---|---|---|
| below -2.0 | serious corrosion | highly aggressive |
| -2.0 to -0.5 | serious corrosion | moderately aggressive |
| -0.5 to below 0 | slightly corrosive, non-scale forming | moderately aggressive |
| 0 | balanced, pitting possible | (boundary) |
| above 0 to 0.5 | slightly scale forming and corrosive | nonaggressive |
| 0.5 to 2 | scale forming, non-corrosive | nonaggressive |
| above 2 | strong scale forming | nonaggressive |
How Is the LSI Calculated? The pHs Formula#
The LSI is calculated as LSI = pH - pHs, where pHs comes from calcium hardness, total alkalinity, TDS and temperature in one of 3 equivalent forms: thermodynamic, APHA with an activity correction, and Carrier's empirical formula.
Thermodynamic form of pHs#
In thermodynamic form, pHs = (pK2 - pKs) + pCa + pAlk: the second dissociation constant of carbonic acid minus the calcite solubility constant, plus the negative logarithms of calcium and alkalinity. The APHA version (1998, cited by Ozair in 2012) adds 5pfm, an activity term that grows with TDS at 25 °C (77 °F): 0.024 at 100 mg/L, 0.044 at 400 mg/L and 0.066 at 1,000 mg/L.
Carrier's formula: factors A, B, C and D#
Carrier's empirical formula computes pHs = (9.3 + A + B) - (C + D), where A corrects for TDS, B for temperature, C for calcium hardness and D for total alkalinity, both as CaCO3. Table 2 shows an illustration water (25 °C, TDS 100 mg/L, calcium and alkalinity 100 mg/L as CaCO3).
| Factor | Corrects for | Equation | Value at the illustration water |
|---|---|---|---|
| A | TDS (mg/L) | (log10 TDS - 1) / 10 | 0.10 |
| B | temperature (°C) | -13.12 x log10(°C + 273) + 34.55 | 2.09 |
| C | calcium hardness (mg/L as CaCO3) | log10(Ca as CaCO3) - 0.4 | 1.60 |
| D | total alkalinity (mg/L as CaCO3) | log10(alkalinity as CaCO3) | 2.00 |
| pHs | (9.3 + A + B) - (C + D) | 7.89 |
Factor B falls from 2.09 at 25 °C (77 °F) to 1.09 at 82 °C (180 °F), so pHs drops about 1 unit.
Which water analysis does the LSI need?#
The LSI needs 5 measured inputs: pH, calcium hardness as CaCO3, total (M) alkalinity as CaCO3, TDS (or conductivity converted to TDS) and the temperature at the point of interest.
Total hardness (2.5 x Ca + 4.12 x Mg, mg/L as CaCO3) used instead of calcium hardness overstates the LSI. Calcium and magnesium are separated under water hardness.
Table 3 lists unit, method edition and trap per input.
| Input | Unit and basis | Method (current edition) | Trap |
|---|---|---|---|
| pH | pH units, at sampling temperature | ASTM D1293-18; analyze within 15 minutes for NPDES (40 CFR 136.3, Table II) | CO2 loss raises pH and inflates the LSI |
| Calcium hardness | mg/L as CaCO3 (1 gpg = 17.1 mg/L, never 17.8) | ASTM D1126-17(2025) (hardness) | total hardness is not calcium hardness |
| Total (M) alkalinity | mg/L as CaCO3 | ASTM D1067-16(2024); SM 2320 B-2021, end point pH 4.5 for NPDES | P alkalinity is not total alkalinity |
| TDS | mg/L (from conductivity, µS/cm, with a stated factor) | ASTM D1125-23 (conductivity) | ppm = mg/L only near density 1 |
| Temperature | °C (°F) at the surface of interest | thermometer | bulk vs tube wall |
Total alkalinity end points are explained under alkalinity of water.
LSI Worked Examples: Cooling Tower, Soft Municipal Water and RO Concentrate#
The 3 worked examples below run the Carrier formula on a cooling tower, a soft municipal water and an RO concentrate, with every input stated.
Worked example 1: cooling tower water at 35 °C (95 °F) and a 60 °C (140 °F) tube wall#
Worked example 1: cooling water at pH 8.2, 35 °C (95 °F), 1,500 mg/L TDS, 400 mg/L calcium hardness (23.4 gpg) and 200 mg/L alkalinity (11.7 gpg) as CaCO3 has pHs 6.91 and LSI +1.29, scale forming. Table 4 compares bulk water and tube wall.
| Step | Equation | Bulk 35 °C (95 °F) | Wall 60 °C (140 °F) |
|---|---|---|---|
| A | (log10 1,500 - 1) / 10 | 0.218 | 0.218 |
| B | -13.12 x log10(T + 273) + 34.55 | 1.900 | 1.456 |
| C | log10 400 - 0.4 | 2.202 | 2.202 |
| D | log10 200 | 2.301 | 2.301 |
| pHs | (9.3 + A + B) - (C + D) | 6.91 | 6.47 |
| LSI | 8.2 - pHs | +1.29 | +1.73 |
| RSI | 2 pHs - 8.2 | 5.63 | 4.74 |
| pHeq | 1.465 x log10 200 + 4.54 | 7.91 | 7.91 |
| PSI | 2 pHs - pHeq | 5.92 | 5.03 |
| AI | 8.2 + log10(200 x 400) | 13.10 | 13.10 |
RSI 5.63, PSI 5.92 and AI 13.10 agree. At the 60 °C (140 °F) wall factor B drops to 1.46 and the LSI reaches +1.73. TDS of 1,500 mg/L exceeds the 800 mg/L limit of Palazzo and co-workers (2015), so the result is a tendency.
Worked example 2: soft municipal water at 15 °C (59 °F)#
Worked example 2: soft municipal water at pH 7.6, 15 °C (59 °F), 250 mg/L TDS, 60 mg/L calcium hardness (3.5 gpg) and 50 mg/L alkalinity (2.9 gpg) as CaCO3 has pHs 8.65 and LSI -1.05: it dissolves calcium carbonate. Table 5 lists the steps.
| Step | Equation | Value |
|---|---|---|
| A | (log10 250 - 1) / 10 | 0.140 |
| B | -13.12 x log10(15 + 273) + 34.55 | 2.283 |
| C | log10 60 - 0.4 | 1.378 |
| D | log10 50 | 1.699 |
| pHs | (9.3 + A + B) - (C + D) | 8.65 |
| LSI | 7.6 - pHs | -1.05 |
| RSI | 2 pHs - 7.6 | 9.69 |
| pHeq | 1.465 x log10 50 + 4.54 | 7.03 |
| PSI | 2 pHs - pHeq | 10.26 |
| AI | 7.6 + log10(50 x 60) | 11.08 |
RSI 9.69 lies above the 7.5 to 8.0 corrosion level and AI 11.08 is moderately aggressive. The 50 mg/L alkalinity clears the 40 mg/L floor of Hach Method 8073, but 15 °C sits below the 25 to 80 °C Palazzo range.
Worked example 3: RO concentrate before and after acid feed#
Worked example 3: an RO feed at pH 7.5, 25 °C (77 °F), 500 mg/L TDS, 100 mg/L calcium and 150 mg/L alkalinity as CaCO3, at 75 % recovery, gives a concentrate LSI (LSIc) of +1.46; 55 mg/L sulfuric acid (as 100 % H2SO4, 459 lb per million gallons) to pH 6.5 brings it to +0.26, and 98 mg/L (817 lb/MG) to pH 6.0 to -0.52.
The method follows the DuPont FilmTec Reverse Osmosis Membranes Technical Manual (form 45-D01504): concentrate pH about 0.5 above feed, pK1 6.35 at 25 °C. Table 6 adds the hydrochloric acid cases.
| Case | Feed pH | Acid dose, as 100 % (mg/L; lb/MG = mg/L x 8.34) | LSIc |
|---|---|---|---|
| No acid | 7.5 | 0 | +1.46 |
| Sulfuric acid | 6.5 | 55 H2SO4 (459) | +0.26 |
| Hydrochloric acid | 6.5 | 41 HCl (342) | +0.26 |
| Sulfuric acid | 6.0 | 98 H2SO4 (817) | -0.52 |
| Hydrochloric acid | 6.0 | 73 HCl (609) | -0.52 |
Against the limits of the same manual (below 0, or below 1 with sodium hexametaphosphate), +1.46 needs a polymeric antiscalant or acid.
This Langelier saturation index arithmetic also runs in the Langelier saturation index calculator, in metric or US units.
Ryznar, Puckorius, Stiff-Davis and 3 Other Saturation Indices Compared#
Six indices complement the LSI: Ryznar, Puckorius and Stiff-Davis reuse pHs for scaling, the Aggressive Index and the Larson-Skold ratio target corrosion, and the CCPP turns saturation into milligrams per liter of calcium carbonate. Table 7 gives each source's own scale; the scales are not interchangeable.
| Index | Formula | Reading | Validity / use | Original reference |
|---|---|---|---|---|
| Langelier saturation index (LSI) | pH - pHs | > 0 deposits CaCO3; < 0 dissolves | pH 6.5 to 9.5 (Veolia); alkalinity > 40 mg/L (Hach); 25 to 80 °C, TDS < 800 mg/L (Palazzo); RO concentrate 10 to 10,000 mg/L TDS (ASTM D3739-19) | Langelier, JAWWA 28(10):1500-1521, 1936 |
| Ryznar Stability Index (RSI) | 2 pHs - pH | ≤ 6.0 scaling increases; > 7.0 scaling may not occur; > 7.5 to 8.0 corrosion probability increases | same inputs as LSI | Ryznar, JAWWA 36(4):472-475, 1944 |
| Puckorius Scaling Index (PSI) | 2 pHs - pHeq; pHeq = 1.465 log10(alkalinity) + 4.54 | < 6 scale; > 6 no scale | cooling water; up to 93 °C (199 °F) | Puckorius and Brooke, Corrosion 47(4):280-284, 1991 |
| Stiff-Davis Stability Index (S&DSI) | pH - (pCa + pAlk + K) | positive = CaCO3 scaling | 0 to 90 °C (32 to 194 °F); ionic strength 0 to 4; RO concentrate > 10,000 mg/L TDS (ASTM D4582-23) | Stiff and Davis, Petroleum Transactions AIME 195:213, 1952 |
| Aggressive Index (AI) | pH + log10(alkalinity x Ca hardness) | ≥ 12 nonaggressive; 10 to 11.9 moderately; < 10 highly aggressive | asbestos-cement pipe; ignores temperature and TDS | Hach Method 8073 (classes) |
| Larson-Skold ratio | (Cl- + 2 SO4 2-) / HCO3- (molar) | higher = more corrosive toward steel | waters near Great Lakes quality | Larson and Skold, JAWWA 49(10), 1957 |
| Calcium carbonate precipitation potential (CCPP) | mg/L CaCO3 to equilibrium | + precipitates; - dissolves; 0 saturated | quantitative complement to the LSI | Merrill and Sanks, JAWWA 70(1):12-18, 1978 |
Ryznar Stability Index (RSI)#
The Ryznar Stability Index is RSI = 2 pHs - pH (J.W. Ryznar, JAWWA, 1944): at or below 6.0 scaling increases, above 7.0 scaling may not occur, and above 7.5 to 8.0 corrosion probability increases (Veolia handbook, chapter 25). Frederick (1990, cited by Ozair in 2012) places approximate saturation at 6.5 to 7.0, a separate scale.
Puckorius Scaling Index (PSI)#
The Puckorius Scaling Index, PSI = 2 pHs - pHeq with pHeq = 1.465 x log10(total alkalinity as CaCO3) + 4.54, reads below 6 as scale forming and above 6 as non-scaling (UFC 3-240-13FN, Appendix B). Puckorius and Brooke developed it for cooling water (Corrosion, 1991); Palazzo gives validity up to 93 °C (199 °F).
Stiff-Davis Stability Index (S&DSI)#
The Stiff-Davis Stability Index, S&DSI = pH - (pCa + pAlk + K), replaces the TDS term with a constant K from ionic strength and temperature, valid from 0 to 90 °C (32 to 194 °F) and ionic strength 0 to 4 (Stiff and Davis, 1952). ASTM D4582-23 applies it to RO concentrates above 10,000 mg/L TDS, where ASTM D3739-19 stops. Oddo-Tomson extends the range to 200 °C (392 °F).
Aggressive Index and Larson-Skold ratio#
The Aggressive Index, AI = pH + log10(alkalinity x calcium hardness), both as CaCO3, rates water nonaggressive at 12 or above, moderately aggressive from 10 to 11.9 and highly aggressive below 10 (Hach Method 8073). It ignores temperature and TDS.
The Larson-Skold ratio, (Cl- + 2 SO4 2-) / HCO3- in molar units, was derived for waters near Great Lakes quality; a higher ratio means more corrosive water toward steel.
Calcium carbonate precipitation potential (CCPP)#
The calcium carbonate precipitation potential is the mg/L of CaCO3 a water would precipitate (positive) or dissolve (negative) to reach equilibrium (Merrill and Sanks, JAWWA, 1978). It answers how much. One remineralization classification (IntechOpen chapter) reads above 10 mg/L as scaling, 3 to 10 protective, -3 to 3 neutral, -10 to -3 mildly corrosive and below -10 aggressive.
What LSI Values Are Typical in Cooling, RO and Drinking Water Systems?#
Target LSI values differ by system: treated cooling water runs well above zero with inhibitors, RO concentrate stays below 0 or 1 depending on the antiscalant, and drinking water is kept from being aggressive. UFC 3-240-13FN Table B-8 rates 11 steps of LSI and the matching RSI or PSI as follows.
| LSI | RSI or PSI | Tendency |
|---|---|---|
| +3.0 | 3.0 | extremely severe scaling |
| +2.0 | 4.0 | very severe scaling |
| +1.0 | 5.0 | severe scaling |
| +0.5 | 5.5 | moderate scaling |
| +0.2 | 5.8 | slight scaling |
| 0.0 | 6.0 | stable |
| -0.2 | 6.5 | very slight dissolving |
| -0.5 | 7.0 | slight dissolving |
| -1.0 | 8.0 | moderate dissolving |
| -2.0 | 9.0 | strong dissolving |
| -3.0 | 10.0 | very strong dissolving |
Cooling towers#
Cooling-tower LSI climbs with cycles: in Table 31-2 of the Veolia Water Technologies Handbook, makeup at LSI -1.2 (RSI 9.4) reaches 0 at 2 cycles, +1.5 at 5, +2.5 at 10 and +3.2 at 15, with pHs taken at 49 °C (120 °F). Inhibited programs hold such values, and each cooling tower water treatment program is compared under cooling tower water treatment.
At 15 cycles the water needs acid: to pH 8.7 it holds LSI +2.5 (RSI 3.7), workable with an inhibitor. Eskom standard 240-55864767 sets a cooling CCPP of 10 to 30 mg/kg as CaCO3.
RO concentrate: LSIc, S&DSI and antiscalants#
RO designs judge the concentrate, not the feed: the DuPont FilmTec manual requires LSIc below 0 without antiscalant and below 1 with 20 mg/L sodium hexametaphosphate in the concentrate, and higher values only with polymeric antiscalants at the supplier's limit. The concentrate rules compare as follows.
| Rule | Value | Source |
|---|---|---|
| LSIc without antiscalant | below 0 | DuPont FilmTec manual 45-D01504 |
| LSIc with 20 mg/L SHMP in the concentrate | below 1 | same manual |
| LSIc above 1 | polymeric antiscalant at the supplier's stated limit | same manual |
| LSIc design target with acid only | -0.2 | Hydranautics TAB-111 |
| Seawater RO | about 10 mg/L H2SO4 for feed pH about 7 and a negative concentrate S&DSI | DuPont FilmTec manual 45-D01504 |
| Index by concentrate TDS | LSI for 10 to 10,000 mg/L; S&DSI above 10,000 mg/L | ASTM D3739-19; ASTM D4582-23 |
The RO antiscalants that allow positive LSIc, with their dose ranges and limits, are compared under RO antiscalants.
Drinking water distribution: aggressive water and corrosion control#
Drinking-water utilities use the LSI and the Aggressive Index to flag aggressive water: an LSI below -2.0 or an AI below 10 is highly aggressive, an LSI from -2.0 to 0 or an AI of 10 to 11.9 moderately aggressive. The rules that frame it compare as follows.
| Instrument | Value | Status |
|---|---|---|
| Directive (EU) 2020/2184, Annex I Part C | water "should not be aggressive"; pH 6.5 to 9.5; conductivity 2,500 µS/cm at 20 °C | indicator values |
| 40 CFR 143.3 | pH 6.5 to 8.5 | US secondary standard, non-enforceable |
| 40 CFR 141.82(f), as amended by LCRI (89 FR 86418, 2024-10-30) | minimum pH 7.0 where the State designates corrosion control parameters | compliance from 2027-11-01 |
| EPA optimal corrosion control treatment manual (2016) | pH 8.8 to 10; DIC 5 to 10 mg C/L for lead | guidance |
Lead and Copper Rule programs based on orthophosphate or pH/DIC are compared under corrosion control treatment.
What Changes the LSI? Chemicals and Operating Conditions#
Five levers move the LSI: pH, alkalinity, calcium, concentration by cycles or recovery, and temperature; scale inhibitors do not change the index but raise how far above it water can run.
pH adjustment: acid and alkali feed#
Acid feed lowers the LSI twice: it lowers pH and converts alkalinity to carbon dioxide, and alkali feed raises it, at the alkalinity changes below (EPA OCCT manual).
| Chemical | Alkalinity change, mg/L as CaCO3 per mg/L |
|---|---|
| Sulfuric acid | -1.02 |
| Hydrochloric acid | -1.37 |
| Caustic soda | +1.25 |
| Lime | +1.35 |
| Soda ash | +0.94 |
| Sodium bicarbonate | +0.60 |
Sulfuric acid adds sulfate (calcium sulfate risk), hydrochloric acid adds chloride (corrosion) (Veolia handbook, chapter 31). Acids and alkalis are compared under pH adjustment chemicals.
Cycles of concentration and tube-wall temperature#
Cycles of concentration raise the LSI because calcium, alkalinity and TDS concentrate as water evaporates, and pH rises with them (7.0 makeup, 8.9 at 10 cycles in Table 31-2).
Calcium carbonate is less soluble when hot (the same handbook, chapter 30), so tube walls scale first: example 1 reaches +1.73 at 60 °C (140 °F).
Raising 3 to 6 cycles cuts makeup 20 % and blowdown 50 % (US DOE FEMP); the LSI limits that gain. The arithmetic of cycles of concentration has its own page.
Scale inhibitors: running above saturation#
Scale inhibitors let cooling water run above saturation: HEDP and ATMP hold about 125 to 150 times calcite saturation (LSI below about 2.0), PBTC about 225 to 250 times (LSI above 2.0 to about 3.0) (Standish, 2024).
Enhanced polymaleic polymers at 8 to 12 mg/L (ppm) as active reach LSI about +2.5 to 3.0.
Each family of scale inhibitors is compared under scale inhibitors.
Where Is the LSI Unreliable? Limits, Other Scales and Common Mistakes#
The LSI is a directional indicator, not a quantity: Veolia limits it to pH 6.5 to 9.5, Hach to waters above 40 mg/L alkalinity, and Palazzo and co-workers to 25 to 80 °C (77 to 176 °F) and TDS below 800 mg/L. The 7 common mistakes are listed below.
- Reading the LSI as mg/L of scale (use CCPP).
- Ignoring alkalinity: Larson (1975) needed LSI 0.9 to precipitate 10 mg/L CaCO3 at 50 mg/L alkalinity, 0.2 at 200 mg/L.
- Reading RSI or PSI on the LSI scale.
- Using total hardness for calcium hardness.
- Using bulk temperature for a tube wall.
- Using the LSI above 10,000 mg/L TDS.
- Expecting coverage of silica, sulfates, phosphate or fluoride scales.
UFC 3-240-13FN says the LSI "has lost its practical application for cooling water systems", and Palazzo et al. (2015) found mild-steel corrosion correlates only moderately with calcium, alkalinity and temperature.
The non-carbonate scales are explained under scale formation in water systems.
How Does the LSI Fit Into Water Treatment Chemistry?#
The LSI links 3 parts of water treatment chemistry: scale formation, which it predicts for calcium carbonate only, corrosion, which it does not measure, and cycles of concentration, which it limits in cooling towers.
The full set of water treatment chemistry concepts sits in one index.
What is a good Langelier saturation index?#
A good LSI depends on the system: drinking water should not be aggressive, an RO concentrate should stay below 0 without antiscalant or below 1 with sodium hexametaphosphate, and inhibited cooling water runs positive up to the inhibitor's ceiling. An untreated system near zero sits at saturation.
What is the difference between LSI and RSI?#
The LSI is pH - pHs and reads around zero, while the RSI is 2 pHs - pH and reads around 6 to 7, so worked example 1 gives LSI +1.29 and RSI 5.63. UFC Table B-8 pairs LSI 0 with RSI 6.0.
Is a negative LSI always corrosive?#
No: a negative LSI means water dissolves calcium carbonate, not that metal corrodes at a given rate, and Carrier's class for an LSI of 0 still notes possible pitting.
Corrosion rates are measured with coupons, covered under corrosion in water systems.