Sodium Adsorption Ratio Calculator

Sodium Adsorption Ratio Formula

Worked Example

Water with 230 mg/L sodium, 60 mg/L calcium and 24 mg/L magnesium:

1. meq/L = mg/L ÷ equivalent weight (Na 22.99, Ca 20.04, Mg 12.15)
2. SAR = Na ÷ √((Ca + Mg)/2) = 10.00444981 ÷ √((2.994161385 + 1.974902283)/2) = 6.34703549

Ca²⁺: 2.994161385 meq/L · Mg²⁺: 1.974902283 meq/L · USDA (Richards) class: low sodium hazard (S1)

GATE tip

Equivalent weight = molar mass ÷ |charge|: Ca²⁺ 40.08/2 = 20.04, Mg²⁺ 24.31/2 = 12.15. The same conversion underlies hardness and alkalinity as CaCO₃ (equivalent weight 50).

More Water Quality Calculators

• Mixing Mass Balance Calculator

  C = (Q₁C₁ + Q₂C₂) / (Q₁ + Q₂)

  flows in any consistent unit; concentrations in any consistent unit

  Example: A river of 10 m³/s with 2 mg/L BOD receiving 0.5 m³/s of effluent at 150 mg/L: Mixed concentration C = 9.04762.

  Open the mixing mass balance calculator →

• Water Hardness Calculator

  TH = 2.497 Ca + 4.118 Mg (mg/L as CaCO₃)

  carbonate hardness = min(TH, alkalinity); non-carbonate = TH − carbonate

  Example: Water with 60 mg/L calcium, 24 mg/L magnesium and 150 mg/L alkalinity: Total hardness = 248.669 mg/L as CaCO₃.

  Open the water hardness calculator →

• BOD Calculator

  BOD_t = L₀(1 − e^(−kt)), BOD₅ = (D₁ − D₂)/P

  k_T = k₂₀ × 1.047^(T − 20); P = sample volume ÷ bottle volume

  Example: Wastewater with ultimate BOD 250 mg/L and k = 0.23 per day at 20 °C, after 5 days: BOD at day 5 = 170.841 mg/L.

  Open the bod calculator →

• Oxygen Sag Curve Calculator

  D_t = (k_d L₀/(k_r − k_d))(e^(−k_d t) − e^(−k_r t)) + D₀e^(−k_r t)

  t_c = ln[(k_r/k_d)(1 − D₀(k_r − k_d)/(k_d L₀))]/(k_r − k_d); D_c = (k_d/k_r)L₀e^(−k_d t_c)

  Example: A river with mixed L₀ = 20 mg/L, D₀ = 1 mg/L, k_d = 0.23 and k_r = 0.46 per day: Critical (maximum) deficit D_c = 5.26316 mg/L.

  Open the oxygen sag curve calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.