Governing Formulas
Both indexes describe whether a water is balanced with respect to CaCO₃. The Langelier Saturation Index (LSI) compares the measured pH with the saturation pH (pH_s) at which the water would be exactly saturated with calcium carbonate. The Ryznar Stability Index (RSI) is a companion empirical index that maps the same saturation pH onto a 0–14 scale.
LSI = pH − pH_s Where:
-
pH= Measured water pH -
T= Water temperature [°C] -
TDS= Total dissolved solids [mg/L] -
[Ca2+]= Calcium hardness as CaCO₃ [mg/L] -
[Alk]= Total alkalinity as CaCO₃ [mg/L] -
A= TDS coefficient: (log₁₀(TDS) − 1) / 10 -
B= Temperature coefficient: −13.12·log₁₀(T+273) + 34.55 -
C= Calcium coefficient: log₁₀([Ca2+]) − 0.4 -
D= Alkalinity coefficient: log₁₀([Alk]) -
pH_s= Saturation pH (9.3 + A + B − C − D) -
LSI= Langelier Saturation Index (pH − pH_s) -
RSI= Ryznar Stability Index (2·pH_s − pH)
Derived Equations:
pH_s = 9.3 + A + B − C − D LSI = pH − pH_s RSI = 2·pH_s − pH
The saturation pH is computed with the four ASTM D3739 coefficients — A from TDS, B from temperature,
C from calcium, and D from alkalinity — exactly as applied in the RO Scaling Risk tool:
pH_s = 9.3 + A + B − C − D.
Interpreting the Results
| Index | Range | Tendency |
|---|---|---|
| LSI = pH − pH_s | > +0.5 | Scaling tendency — CaCO₃ will tend to deposit. |
| −0.5 … +0.5 | Near saturation — generally stable. | |
| < −0.5 | Corrosive tendency — CaCO₃ tends to dissolve. | |
| RSI = 2·pH_s − pH | < 6 | Scaling tendency. |
| 6 … 7 | Generally stable. | |
| > 7 | Corrosive tendency. |
LSI and RSI usually agree, but they occasionally point in different directions on the same sample — the tendency bands above handle that by reporting each index independently. Neither index is a treatment prescription: real dosing decisions belong to a treatment specialist.
How to Use This Calculator
- Enter the measured water pH (0–14).
- Enter the sample temperature — this drives coefficient B.
- Enter TDS in mg/L — used for coefficient A and the µ estimate.
- Enter calcium hardness as CaCO₃ and total alkalinity as CaCO₃ in mg/L.
Typical reference points (as CaCO₃)
Municipal potable waters commonly sit around pH 7–8, Ca 40–120 mg/L, alkalinity 50–200 mg/L, where LSI usually lands in or near the balanced band. Waters at high pH with high hardness and alkalinity drift into the scaling band; soft, low-alkalinity waters at low pH drift into the corrosive band.
Accuracy Limits & Method Notes
- LSI is a saturation tendency, not a corrosion or scaling rate. Speciation, temperature effects, inhibitors, and exact salt matrix change the outcome.
- The ASTM D3739 model is tuned for fresh/brackish waters; for seawater-salinity samples use the Stiff & Davis index in the RO Scaling Risk tool.
- Ionic strength is estimated from TDS (µ ≈ 2.5×10⁻⁵ × TDS); a measured ionic strength is more accurate.
Frequently Asked Questions
What is the difference between LSI and RSI?
Both use the same saturation pH. LSI = pH − pH_s is positive when the water can deposit CaCO₃. RSI = 2·pH_s − pH is inverted (low value means scaling) and is used because some operators find the 0–14 scale more intuitive. They are companions, not substitutes.
Is LSI 0 perfectly balanced?
LSI = 0 means the water is exactly saturated with CaCO₃ at the measured conditions. In practice a range from about −0.5 to +0.5 is treated as acceptably stable; beyond that, waters are considered scale-forming or corrosive enough to matter for piping and equipment.
Should I use LSI or the Stiff–Davis index for seawater?
For seawater and very high-TDS brines use the Stiff & Davis Stability Index, which replaces the TDS approximation with measured ionic strength. Use the RO Scaling Risk tool for that. LSI here follows ASTM D3739, which is appropriate for fresh and brackish finished waters.
Engineering Disclaimer
Engineering Note: LSI and RSI indicate the equilibrium tendency of a water with respect to calcium carbonate; they do not quantify scaling or corrosion rates and are not a substitute for a certified water analysis or treatment-vendor projection.
Technical References
- ASTM D3739-19: Standard Practice for Calculation and Adjustment of the Langelier Saturation Index for Reverse Osmosis Process Design, ASTM International.
- Ryznar, J. W. (1944). A New Index for Determining Amount of Calcium Carbonate Scale Formed by a Water. Journal AWWA, 36(4), 472–483.