BOD Calculator
Wastewater with an ultimate BOD of 250 mg/L and k = 0.23 per day exerts 170.841 mg/L of BOD in five days at 20 °C, about 68 % of its ultimate demand.
170.840807655237 mg/L
Full answer, then cut to fewer decimals (not rounded):
- 170.840807655237 mg/L
- 170.84080765523 mg/L
- 170.8408076552 mg/L
- 170.840807655 mg/L
- 170.84080765 mg/L
- 170.8408076 mg/L
- 170.840807 mg/L
- 170.84080 mg/L
- 170.8408 mg/L
- 170.840 mg/L
- 170.84 mg/L
- 170.8 mg/L
- Rate constant at 20 °C
- 0.23 per day
- Remaining BOD L_t = L₀e^(−kt)
- 79.15919234 mg/L
- Base-10 rate constant k/2.303
- 0.09988773084 per day
Step-by-step solution
- k_T = k₂₀ × 1.047^(T − 20) = 0.23 per day
- BOD_t = L₀(1 − e^(−kt)) = 250 × (1 − e^(−1.15)) = 170.8408077 mg/L
BOD Formula
BOD_t = L₀(1 − e^(−kt)), BOD₅ = (D₁ − D₂)/P
k_T = k₂₀ × 1.047^(T − 20); P = sample volume ÷ bottle volume
Worked Example
Wastewater with ultimate BOD 250 mg/L and k = 0.23 per day at 20 °C, after 5 days:
- k_T = k₂₀ × 1.047^(T − 20) = 0.23 per day
- BOD_t = L₀(1 − e^(−kt)) = 250 × (1 − e^(−1.15)) = 170.8408077 mg/L
Remaining BOD L_t = L₀e^(−kt): 79.15919234 mg/L · Base-10 rate constant k/2.303: 0.09988773084 per day
GATE tip
For mixtures, BOD and ultimate BOD both mix by flow-weighted averages: L₀,mix = (Q_r L_r + Q_w L_w)/(Q_r + Q_w). Compute the mixed L₀ before using it in the Streeter–Phelps equation.
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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.
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C = (Q₁C₁ + Q₂C₂) / (Q₁ + Q₂)
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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.
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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.
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TH = 2.497 Ca + 4.118 Mg (mg/L as CaCO₃)
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Example: Water with 60 mg/L calcium, 24 mg/L magnesium and 150 mg/L alkalinity: Total hardness = 248.669 mg/L as CaCO₃.
Frequently asked questions
Why is BOD measured over five days?
Five days at 20 °C was chosen in Britain because no river took longer to reach the sea; by then most carbonaceous demand of domestic sewage (about two thirds) is exerted.
Base e or base 10 rate constant?
Textbooks use both: k (base e) = 2.303 × K (base 10). This calculator uses base e and shows the base-10 value too.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). BOD Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/bod-calculator/
IEEE
Scientific Converters, "BOD Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/bod-calculator/