Water Operator Math: the Formulas & Conversions Cheat Sheet

Conversions to know cold

1 ft³	7.48 gal
1 gal of water	weighs 8.34 lb
1 MGD	694 gpm · 1.547 cfs
1 cfs	448.8 gpm
1 ft of head	0.433 psi
1 psi	2.31 ft of head
Circle area	0.785 × d²
Circumference	3.14 × d

The formulas

Pounds formula (chemical feed)

lb/day = flow (MGD) × dose (mg/L) × 8.34
Solve for any one variable — dose (mg/L) = lb/day ÷ (MGD × 8.34). The most-used formula on the exams; it drives chlorine, alum, and fluoride feed questions.

Pressure and head

psi = head (ft) × 0.433 · head (ft) = psi × 2.31
Static pressure under an elevated tank; pump head conversions.

Pipe volume

V = 0.785 × d² × L (d and L in feet gives ft³) · gal = ft³ × 7.48
Convert inches to feet first: a 6-inch main has d = 0.5 ft.

Tank volume

Rectangular: V = L × W × H · Cylindrical: V = 0.785 × d² × depth · gal = ft³ × 7.48
Basins, clarifiers, wet wells, and storage tanks.

Detention time

DT = volume ÷ flow
Keep the units consistent: gal ÷ gpm = minutes; gal ÷ gph = hours.

Velocity

V = Q ÷ A
Flow (ft³/s) divided by cross-sectional area (ft²) gives velocity in ft/s.

Surface loading rate

gpd/ft² = flow (gpd) ÷ surface area (ft²)
Clarifier and sedimentation-basin overflow rates.

Weir loading

gpd per ft = flow (gpd) ÷ weir length (ft)
For a circular clarifier, the weir length is the circumference: 3.14 × diameter.

Horsepower

Water hp = (gpm × head in ft) ÷ 3,960 · Brake hp = water hp ÷ efficiency
Efficiency as a decimal (85% = 0.85).

Chlorine dose

Dose = demand + residual
Given the dose applied and the residual measured, demand = dose − residual.

Dilution / solution strength

C1 × V1 = C2 × V2
Preparing a weaker solution from a stronger stock.

Sewer slope (collection systems)

Slope (%) = (fall ÷ run) × 100
Fall = upstream invert elevation − downstream invert elevation, in feet; run = pipe length in feet.

Worked examples

These four are taken from TradeQBank's free sample questions — each bank's free sample is linked from pricing.

• Chlorine feed: 0.75 MGD × 2.0 mg/L × 8.34 = 12.5 lb/day.
• Detention time: 60,000 gal ÷ 500 gpm = 120 min = 2.0 hr.
• Static pressure: 80 ft of head × 0.433 = 34.6 psi, about 35 psi.
• Pipe volume: 0.785 × (0.5 ft)² × 500 ft = 98.1 ft³; 98.1 × 7.48 = 734 gal in a 500-ft section of 6-inch main.

Where these come from

The formulas and conversions above are the ones used by the calculation questions in our seven practice banks (235 calculation questions out of 2,282 total). Their cited sources are the WPI (ABC) Formula/Conversion Table — the same table administered with the exams — and the California State University, Sacramento operator references: Water Treatment Plant Operation Vols. 1–2, Water Distribution System Operation and Maintenance, Operation of Wastewater Treatment Plants, and Operation and Maintenance of Wastewater Collection Systems. Every bank question carries its citation, and every answer key passed an independent second verification before publishing — see Our Method.

Formulas alone don't pass the exam — recognizing which one a question calls for does. The full banks drill all 235 calculation questions with worked explanations: see the banks and pricing, or start with a free 25-question sample and get a per-area score breakdown at the end.