Langelier Saturation Index

LSI = pH − pHs
pHs = pK₂ − pKs + p[Ca] + p[Alk] + 5·pfm
pK₂, pKs (calcite) = f(T), Plummer & Busenberg 1982
pfm = A(√I / (1 + √I) − 0.3·I)
A = 1.82·10⁶ (E·T)^−1.5, E = 60954 / (T + 116) − 68.937
I ≈ 2.5·10⁻⁵ × TDS

• Standard Methods for the Examination of Water and Wastewater, 2330 B Calcium Carbonate Saturation (APHA, AWWA, WEF)
  Saturation index and the simplified pHs equation. Checked against the worked example of the method: pK₂ 10.38, pKs 8.45, pfm 0.063 at 20 °C.
• USGS PHREEQC databases phreeqc.dat and wateq4f.dat
  Temperature equations for pK₂ and calcite pKs (Plummer & Busenberg 1982). Independent check: on 185 random waters this calculator differs from a full PHREEQC calculation by 0.02 on average, at most 0.12.
• Government of Newfoundland and Labrador, Calculation of the Langelier Index
  Ionic strength from TDS (2.5·10⁻⁵ × TDS) and the form of the constant A. Here the dielectric constant of water depends on temperature; at 20 °C this gives A = 0.506, the value used in the Standard Methods example.
• US Patent 8,721,898 B2 (2014)
  Quick Carrier formula, shown for comparison only. It differs from the full calculation by up to 0.27 on the same 185 waters.

• LSI below 0: water is undersaturated with calcium carbonate and tends to remove existing scale. Above 0: scale may form (USBR 2013).
• The simplified Standard Methods equation holds for pH 6.0–8.5 and alkalinity above about 50 mg/L as CaCO₃. Outside this range the calculator shows a warning.
• Calcium ion pairs and non-carbonate alkalinity are neglected, as in the hand method of Standard Methods. Full water chemistry codes give slightly lower values.
• Ionic strength is estimated from TDS. If you have a full ion analysis, the result can be refined.
• For RO concentrate above 10,000 mg/L TDS use the Stiff & Davis index (ASTM D4582).
• The index shows a tendency. It does not predict how fast scale forms or how much.