Every formula you need for the wastewater operator certification exam — organized by category, with the exact notation used on the ABC/WPI formula sheet. Bookmark this page.
| Area of Circle | (0.785)(Diameter²) also: (3.14)(Radius²) |
| Circumference of Circle | (3.14)(Diameter) |
| Area of Rectangle | (Length)(Width) |
| Area of Right Triangle | (Base)(Height) ÷ 2 |
| Volume of Rectangular Tank | (Length)(Width)(Height) |
| Volume of Cylinder | (0.785)(Diameter²)(Height) |
| Volume of Cone | (1/3)(0.785)(Diameter²)(Height) |
| Area of Cylinder (total exterior) | [End #1 SA] + [End #2 SA] + [(3.14)(Diameter)(Height)] SA = surface area of each circular end |
| Flow Rate | Q = (Area, ft²)(Velocity, ft/sec) Result in ft³/sec |
| Velocity | Flow Rate (ft³/sec) ÷ Area (ft²) also: Distance (ft) ÷ Time (sec) |
| Detention Time | Volume ÷ Flow Units must be compatible — convert flow to match volume units |
| Slope, % | (Drop or Rise ÷ Distance) × 100% |
| Removal, % | [(In − Out) ÷ In] × 100% |
| Return Rate, % | (Return Flow Rate ÷ Influent Flow Rate) × 100% |
| Recirculation Ratio (Trickling Filter) | Recirculated Flow ÷ Primary Effluent Flow |
| Loading Rate, lb/day | (Flow, MGD)(Concentration, mg/L)(8.34 lb/gal) The "pounds formula" — the most-used calculation in wastewater math |
| Mass, lb | (Volume, MG)(Concentration, mg/L)(8.34 lb/gal) |
| Hydraulic Loading Rate, gpd/ft² | Total Flow Applied (gpd) ÷ Area (ft²) |
| Surface Overflow Rate (SOR), gpd/ft² | Flow (gpd) ÷ Area (ft²) |
| Weir Overflow Rate, gpd/ft | Flow (gpd) ÷ Weir Length (ft) |
| Solids Loading Rate, lb/day/ft² | Solids Applied (lb/day) ÷ Surface Area (ft²) |
| Organic Loading Rate — Trickling Filter, lb BOD/day/1,000 ft³ | Organic Load (lb BOD₅/day) ÷ Volume (1,000 ft³) |
| Population Equivalent (Organic) | (Flow, MGD)(BOD, mg/L)(8.34 lb/gal) ÷ 0.17 lb BOD/day/person |
| BOD₅ (unseeded), mg/L | [(Initial DO − Final DO)(300 mL)] ÷ Sample Volume (mL) 300 mL = standard BOD bottle volume |
| BOD₅ (seeded), mg/L | [(Initial DO − Final DO − Seed Correction)(300 mL)] ÷ Sample Volume (mL) Seed correction accounts for DO consumed by the seed itself |
| BOD Loading, lb/day | (Flow, MGD)(BOD, mg/L)(8.34 lb/gal) |
| BOD Removal, % | [(Influent BOD − Effluent BOD) ÷ Influent BOD] × 100% |
| Oxygen Uptake Rate (OUR), mg/L/min | Oxygen Usage (mg/L) ÷ Time (min) |
| Specific Oxygen Uptake Rate (SOUR), (mg/g)/hr | (OUR, mg/L/min)(60 min) ÷ (MLVSS, g/L)(1 hr) |
| Sludge Volume Index (SVI), mL/g | (SSV₃₀, mL/L)(1,000 mg/g) ÷ MLSS (mg/L) SSV₃₀ = settled sludge volume at 30 minutes in settleometer |
| Sludge Density Index (SDI) | 100 ÷ SVI |
| Food/Microorganism Ratio (F/M) | BOD₅ (lb/day) ÷ MLVSS (lb) Use MLVSS — not MLSS — in the denominator |
| Mean Cell Residence Time (MCRT) or Solids Retention Time (SRT), days | [Aeration Tank TSS (lb) + Clarifier TSS (lb)] ÷ [TSS Wasted (lb/day) + Effluent TSS (lb/day)] MCRT = SRT = sludge age — all the same thing |
| Return Sludge Rate (Solids Balance), MGD | (MLSS, mg/L)(Flow Rate, MGD) ÷ [(RAS SS, mg/L) − (MLSS, mg/L)] |
| Volatile Solids, % | [(Dry Solids − Fixed Solids) ÷ Dry Solids] × 100% |
| Reduction of Volatile Solids, % | [(VS in − VS out) ÷ (VS in − VS in × VS out)] × 100% All values expressed as decimals (VS in fraction form) |
| Total Solids, % | [(Dried Weight − Tare Weight) ÷ (Wet Weight − Tare Weight)] × 100% |
| Solids, mg/L | (Dry Solids, g)(1,000,000) ÷ Sample Volume (mL) |
| Solids Capture, % (Centrifuge) | [(Cake TS%)(Feed TS% − Centrate TSS%)] ÷ [(Feed TS%)(Cake TS% − Centrate TSS%)] × 100% |
| Feed Rate, lb/day | (Dosage, mg/L)(Flow, MGD)(8.34 lb/gal) ÷ Purity (decimal) Purity expressed as decimal — e.g., 65% pure = 0.65 |
| Chemical Feed Pump Setting, % Stroke | (Desired Flow ÷ Maximum Flow) × 100% |
| Chemical Feed Pump Setting, mL/min | (Flow, MGD)(Dose, mg/L)(3.785 L/gal)(1,000,000 gal/MG) ÷ (Feed Chemical Density, mg/mL)(Active Chemical, decimal)(1,440 min/day) |
| Blending / Three Normal Equation | (C₁ × V₁) + (C₂ × V₂) = (C₃ × V₃) Where V₁ + V₂ = V₃. Concentration units must match. Volume units must match. |
| Dilution / Two Normal Equation | (C₁ × V₁) = (C₂ × V₂) C = concentration, V = volume or flow |
| Specific Gravity | Specific Weight of Substance (lb/gal) ÷ 8.34 lb/gal |
| Alkalinity, mg/L as CaCO₃ | (Titrant Volume, mL)(Acid Normality)(50,000) ÷ Sample Volume (mL) |
| Hardness, mg CaCO₃/L | (Titrant Volume, mL)(1,000) ÷ Sample Volume (mL) Only when titration factor is 1.00 of EDTA |
| Composite Sample Single Portion | (Instantaneous Flow)(Total Sample Volume) ÷ (Number of Portions)(Average Flow) |
| Cycle Time, min (wet well) | Storage Volume (gal) ÷ [Pump Capacity (gpm) − Wet Well Inflow (gpm)] |
| Water Horsepower (WHP) | (Flow, gpm)(Head, ft) ÷ 3,960 Theoretical power with 100% efficiency — always the lowest HP value |
| Brake Horsepower (BHP) | (Flow, gpm)(Head, ft) ÷ (3,960)(Pump Efficiency, decimal) Actual power needed at the pump shaft |
| Motor Horsepower (MHP) | (Flow, gpm)(Head, ft) ÷ (3,960)(Pump Efficiency, decimal)(Motor Efficiency, decimal) Power drawn from the electrical supply — always the highest HP value |
| Motor Efficiency, % | (Brake HP ÷ Motor HP) × 100% |
| Wire-to-Water Efficiency, % | (Water HP ÷ Motor HP) × 100% also: (Flow, gpm)(TDH, ft)(0.746 kW/hp)(100%) ÷ (3,960)(Electrical Demand, kW) |
| Force, lb | (Pressure, psi)(Area, in²) |
| Electromotive Force (EMF), Volts | (Current, amps)(Resistance, ohms) — E = IR |
| Amps | Volts ÷ Ohms |
| Watts (DC) | (Volts)(Amps) |
| Watts (AC) | (Volts)(Amps)(Power Factor) |
| Power, kW | (Flow, L/sec)(Head, m)(9.8) ÷ 1,000 |
| Filter Backwash Rate, gpm/ft² | Flow (gpm) ÷ Filter Area (ft²) |
| Filter Backwash Rise Rate, in/min | (Backwash Rate, gpm/ft²)(12 in/ft) ÷ 7.48 gal/ft³ |
| Filter Yield, lb/hr/ft² | (Solids Loading, lb/day)(Recovery, decimal) ÷ (Filter Operation, hr/day)(Area, ft²) |
| Weir Overflow Rate, gpd/ft | Flow (gpd) ÷ Weir Length (ft) |
| Surface Overflow Rate (SOR), gpd/ft² | Flow (gpd) ÷ Surface Area (ft²) Primary clarifier typical: 600–1,200 gpd/ft² |
| Coliform Count, CFU/100 mL | (# of Colonies on Plate × 100) ÷ Sample Volume (mL) |
| Solids Concentration, mg/L | Weight (mg) ÷ Volume (L) |
| Solids, mg/L (from dried weight) | (Dry Solids, g)(1,000,000) ÷ Sample Volume (mL) |
| Arithmetic Mean (Average) | Sum of All Terms ÷ Number of Terms |
| Geometric Mean | [(X₁)(X₂)(X₃)...(Xn)]^(1/n) nth root of the product of n numbers — used for coliform averaging |
| Milliequivalent | (mL)(Normality) |
| Molarity | Moles of Solute ÷ Liters of Solution |
| Normality | Equivalent Weights of Solute ÷ Liters of Solution |
| Degrees Celsius | (°F − 32) ÷ 1.8 |
| Degrees Fahrenheit | (°C)(1.8) + 32 |
| Key temperatures to know | BOD test: 20°C (68°F) · Mesophilic digestion: 35°C (95°F) · Thermophilic digestion: 55°C (131°F) |
| 1 gallon (US) | = 3.785 L = 8.34 lb |
| 1 cubic foot of water | = 7.48 gal = 62.4 lb |
| 1 cubic foot per second | = 0.646 MGD = 448.8 gpm |
| 1 MGD | = 694 gpm = 1.55 ft³/sec |
| 1 acre | = 43,560 ft² |
| 1 acre-foot | = 326,000 gal |
| 1 foot of water | = 0.433 psi |
| 1 psi | = 2.31 ft of water = 6.89 kPa |
| 1 atmosphere | = 14.7 psi = 33.9 ft water |
| 1 horsepower | = 0.746 kW = 746 W |
| 1 foot | = 0.305 m |
| 1 inch | = 2.54 cm |
| 1 pound | = 0.454 kg |
| 1 ton | = 2,000 lb |
| 1 metric ton | = 2,205 lb = 1,000 kg |
| 1 grain/gal | = 17.1 mg/L |
| 1 liter/second | = 0.0864 MLD |
| 1% | = 10,000 mg/L |
| π (pi) | = 3.14 |
The WastewaterAce Complete Exam Guide includes 200 practice questions — many requiring you to apply these formulas in real exam scenarios. Full explanations with every answer.
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