Wastewater Operator Formula Sheet
See every one of these formulas worked in exam style in the Grade 2 exam review.
Most certifying bodies supply a formula sheet at the exam. That's not a reason to skip memorizing these — a formula you have to look up is a formula you don't really understand, and the exam tests whether you know which one applies, not whether you can copy it. Read this to learn the relationships. Use the formula calculator to check your work while practicing, and the SVI calculator when you want the interpretation as well as the number.
▶ Watch: Wastewater Operator Exam Cheat Sheet: Formula Review
Conversion Factors to Memorize
These show up inside other formulas rather than as questions of their own. Not knowing them cold is the most expensive gap on the math portion.
| Quantity | Value |
|---|---|
| Weight of water | 8.34 lb/gal |
| Cubic foot of water | 7.48 gal · 62.4 lb |
| Horsepower | 746 watts · 33,000 ft-lb/min |
| Pressure to head | 1 psi = 2.31 ft of head |
| Head to pressure | 1 ft of head = 0.433 psi |
| Acre | 43,560 ft² |
| Acre-foot | 325,829 gal |
| Million gallons | 1 MG = 1,000,000 gal · 1 mgd = 694.4 gpm |
| Pi | 3.14 · area of a circle = 0.785 × D² |
| Percent to decimal | divide by 100 · 1% ≈ 10,000 mg/L |
| Day | 1,440 minutes · 86,400 seconds |
One gallon of water weighs 8.34 pounds. That single number is buried inside the pounds formula, chemical dosing, solids loading, F/M, MCRT, and most of the loading calculations. If you remember one thing from this page, remember what 8.34 is — not just where to plug it in. Every "pounds per day" question on the exam is the same question wearing different clothes.
The Pounds Formula
This is the most-used formula in wastewater. It converts a concentration into a mass, which is what actually matters operationally — a plant doesn't remove milligrams per liter, it removes pounds.
Every one of these is the pounds formula in disguise:
- BOD loading — flow × influent BOD × 8.34
- Solids inventory — volume in MG × MLSS × 8.34
- Chemical feed — flow × dose × 8.34
- Solids wasted per day — WAS flow × WAS concentration × 8.34
Flow, Detention & Loading
| Formula | Expression | Watch for |
|---|---|---|
| Flow rate | Q = Velocity × Area | Area in ft², velocity in ft/sec gives ft³/sec — convert with 7.48 |
| Velocity | V = Distance ÷ Time | Common on collections questions as travel time in a sewer |
| Detention time | DT = Volume ÷ Flow | Gallons ÷ gpd = days. ×24 for hours, ×1,440 for minutes |
| Hydraulic loading rate | HLR = Flow ÷ Area | gpd/ft² — used on filters and ponds |
| Surface overflow rate | SOR = Flow ÷ Surface area | Influent flow only — no RAS |
| Weir overflow rate | WOR = Flow ÷ Weir length | gpd/ft. Circular weir length = π × D |
| Solids loading rate | SLR = (Q + RAS) × MLSS × 8.34 ÷ Area | Includes RAS flow — this is the trap |
| Backwash rate | Flow ÷ Filter area | gpm/ft² |
Both describe a clarifier. Surface overflow rate uses influent flow only, because it's describing the upward velocity of water. Solids loading rate adds RAS flow, because both streams carry solids into the clarifier. Candidates who miss this usually get SOR right and SLR wrong — and the answer choices are written to reward the mistake.
Process Control
| Formula | Expression | Units / notes |
|---|---|---|
| F/M ratio | BOD lbs/day ÷ MLVSS lbs | Note MLVSS, not MLSS. Food over microorganisms. |
| SVI | (SSV₃₀ mL/L ÷ MLSS mg/L) × 1,000 | mL/g. Normal 80–150. Calculator |
| SDI | 100 ÷ SVI | Sludge density index — the inverse relationship |
| MCRT / SRT | MLSS lbs in system ÷ (WAS lbs/day + effluent TSS lbs/day) | Days. Effluent solids count as leaving the system |
| Return rate | (RAS flow ÷ Influent flow) × 100 | Percent |
| Removal efficiency | [(In − Out) ÷ In] × 100 | Percent. Works for BOD, TSS, anything |
| Volatile solids | (VS ÷ TS) × 100 | Percent volatile — the organic fraction |
| Sludge age (Gould) | MLSS lbs ÷ Suspended solids added lbs/day | Days — a simpler alternative to MCRT |
Not interchangeable, and exams test the distinction. F/M measures food against living biomass, so it uses volatile suspended solids. SVI measures how a given mass of total solids settles, so it uses MLSS. Reading the question for which one it gives you is half the work.
Dosing & Mass
| Formula | Expression | Watch for |
|---|---|---|
| Chemical feed, 100% pure | lbs/day = Flow (MGD) × Dose (mg/L) × 8.34 | The pounds formula again |
| Feed rate, adjusted for purity | lbs/day ÷ (% purity ÷ 100) | Divide by purity — 65% HTH means more product, not less |
| Chlorine dose | Dose = Demand + Residual | Rearranges three ways; know all three |
| Feed pump setting | Based on solution strength and pump capacity | Check whether the question wants gpd or mL/min |
| Loading rate | lbs/day ÷ Area or Volume | Units follow whatever it's loaded against |
Laboratory
| Formula | Expression |
|---|---|
| Alkalinity as CaCO₃ | (mL titrant × acid normality × 50,000) ÷ sample mL |
| Hardness as CaCO₃ | (mL titrant × 1,000) ÷ sample mL |
| BOD, unseeded | (Initial DO − Final DO) × Dilution factor |
| Dilution factor | Total volume ÷ Sample volume |
| Solids concentration | (Dry weight ÷ Sample volume) × 1,000,000 → mg/L |
| Colony count | (Colonies counted ÷ mL sample) × 100 → per 100 mL |
Lab formulas trip people on sample volume, not on the math. Read whether the question gives you 50 mL, 100 mL, or 1 L before you start — the 50,000 in the alkalinity formula already assumes the conversion, and doubling it because you also converted is a classic error.
Geometry
| Shape | Formula |
|---|---|
| Area of a circle | 0.785 × D² (or πr²) |
| Circumference | π × D |
| Area of a rectangle | Length × Width |
| Area of a right triangle | (Base × Height) ÷ 2 |
| Volume of a cylinder | 0.785 × D² × Height |
| Volume of a cone | (0.785 × D² × Height) ÷ 3 |
| Volume of a rectangular tank | Length × Width × Depth |
Volumes come out in cubic feet. Multiply by 7.48 for gallons — that step is where most tank-volume questions are actually won or lost.
Electrical & Pumping
| Formula | Expression |
|---|---|
| Water horsepower | (Flow gpm × Head ft) ÷ 3,960 |
| Brake horsepower | WHP ÷ Pump efficiency |
| Motor horsepower | BHP ÷ Motor efficiency |
| Wire-to-water efficiency | Pump efficiency × Motor efficiency |
| Electromotive force | E = I × R |
| Power, AC circuit | Watts = Volts × Amps × Power factor |
| Force | Pressure × Area |
Water horsepower is the work actually delivered to the water. Brake horsepower is what the pump shaft needs. Motor horsepower is what the motor draws. Each step divides by an efficiency, so each number gets larger as you move back toward the power source. If your motor horsepower came out smaller than your water horsepower, you divided in the wrong direction.
The Unit Traps
| Trap | What happens |
|---|---|
| gpd vs. MGD | The pounds formula wants MGD. Feeding it 500,000 gpd instead of 0.5 gives an answer a million times too large. |
| Forgetting RAS in SLR | Answer looks plausible and is wrong. See the SOR/SLR box above. |
| MLSS where MLVSS belongs | F/M comes out low. The question gives you both for a reason. |
| Cubic feet left unconverted | Volume answers off by a factor of 7.48. |
| Percent left as a percent | 65% purity is 0.65 in the calculation. |
| Radius vs. diameter | 0.785 × D² uses diameter. πr² uses radius. Mixing them is off by 4×. |
| Detention time in wrong units | Volume ÷ flow gives days. The question usually wants hours. |
| Dividing instead of multiplying by efficiency | See the horsepower chain. |
Write the units next to every number before you calculate. If the units don't cancel to what the answer needs, the setup is wrong and no amount of arithmetic will save it. Operators who do this consistently outperform operators who are faster at math — the exam punishes setup errors far more than calculation errors.
Practice, Don't Just Read
A formula sheet is a reference, not a study method. You learn these by working problems until the setup becomes automatic. Two things on this site that help:
- The formula calculator — all 39 formulas above, solving for any variable, so you can check work instantly instead of hunting for an arithmetic slip.
- Worked math problems — the same formulas applied to exam-style questions, step by step.
200 Questions. 12 Topics. Zero Math.
Knowing the formulas is half of it — the other half is the conceptual material that makes up most of the exam. The Complete Exam Guide covers all 12 topics with a detailed explanation behind every answer.
Get the Complete Exam Guide — $17Instant PDF download · 200 questions · Answer key included