Water Hardness Calculator

Water Hardness Formula

Worked Example

Water with 60 mg/L calcium, 24 mg/L magnesium and 150 mg/L alkalinity:

1. Ca hardness = 60 × 50.04/20.04 = 149.8383153
2. Mg hardness = 24 × 50.04/12.15 = 98.83102242
3. Total = 248.6693377 mg/L as CaCO₃; carbonate hardness = min(TH, alkalinity) = 150

Magnesium hardness 4.118 × Mg: 98.83102242 mg/L as CaCO₃ · Carbonate (temporary) hardness: 150 mg/L as CaCO₃ · Non-carbonate (permanent) hardness: 98.66933771 mg/L as CaCO₃ · In German degrees (°dH): 13.93261641 · Classification (USGS): very hard

GATE tip

In lime–soda softening, lime removes carbonate hardness and magnesium; soda ash removes non-carbonate calcium hardness. Splitting the hardness first sets the chemical doses.

More Water Quality Calculators

• Sodium Adsorption Ratio Calculator

  SAR = Na / √((Ca + Mg)/2)

  concentrations in meq/L; mg/L ÷ equivalent weight (Na 22.99, Ca 20.04, Mg 12.15)

  Example: Water with 230 mg/L sodium, 60 mg/L calcium and 24 mg/L magnesium: Sodium adsorption ratio SAR = 6.34704.

  Open the sodium adsorption ratio 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 →

• 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 →

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.