Skip to content

Operator formula sheets

The formulas for all four certification tracks, in plain operator notation, on one page.

Print this page. Each sheet starts on its own page.

Water treatment formula sheet

This is the reference, in plain operator notation, for the math on the water treatment exam. The exam is closed book but hands you a sheet much like this, so study from it until you know where each formula lives. The teaching behind each one is on the water treatment math page.

Conversions and constants

  • 1 cubic foot = 7.48 gallons
  • 1 gallon of water = 8.34 pounds
  • 1 MGD = 694 gallons per minute = 1.55 cubic feet per second
  • 1 cubic foot per second = 448.8 gallons per minute
  • 1 day = 1,440 minutes
  • 1 psi = 2.31 feet of water; 1 foot of water = 0.433 psi
  • 1 percent = 10,000 mg/L; 1 grain per gallon = 17.1 mg/L
  • 0.785 = pi divided by 4; 8.34 = pounds per gallon

Geometry, flow, and detention

  • Area of a circle = 0.785 × diameter squared
  • Volume of a cylinder in gallons = 0.785 × diameter squared × depth × 7.48
  • Volume of a rectangle in gallons = length × width × depth × 7.48
  • Flow = area × velocity
  • Detention or contact time = volume ÷ flow

Dosage and chemical feed

  • Pounds per day = concentration (mg/L) × flow (MGD) × 8.34
  • Chlorine dose = demand + residual
  • Dry chemical pounds per day = pounds needed ÷ (available percent ÷ 100)
  • Liquid gallons per day = pounds needed ÷ (strength fraction × weight in pounds per gallon)
  • Blending: concentration one × volume one = concentration two × volume two

Sedimentation and filtration

  • Surface overflow rate = flow in gallons per day ÷ surface area in square feet
  • Weir overflow rate = flow in gallons per day ÷ weir length in feet
  • Filtration rate = flow in gallons per minute ÷ filter area in square feet
  • Percent removal = (influent minus effluent) ÷ influent × 100

Disinfection and CT

  • CT = chlorine residual (mg/L) × contact time (minutes)
  • Inactivation ratio = actual CT ÷ required CT; at or above 1.0 the requirement is met

Wells, pressure, and pumps

  • Drawdown = pumping level minus static level
  • Specific capacity = well yield in gallons per minute ÷ drawdown in feet
  • Water horsepower = (gallons per minute × head in feet) ÷ 3,960
  • Brake horsepower = water horsepower ÷ pump efficiency
  • Motor horsepower = brake horsepower ÷ motor efficiency

Use it

Study from this sheet, but work the problems on the water treatment math page by hand and run them in the operator calculator. Confirm your state's exam allows a basic calculator on your state's page.

Water distribution formula sheet

Plain-notation reference for the distribution exam math. The exam is closed book, but it provides a sheet like this one, so learn where each formula sits. The worked teaching is on the water distribution math page.

Conversions and constants

  • 1 cubic foot = 7.48 gallons; 1 gallon of water = 8.34 pounds
  • 1 MGD = 694 gallons per minute = 1.547 cubic feet per second
  • 1 cubic foot per second = 448.8 gallons per minute
  • 1 mile = 5,280 feet; 1 day = 1,440 minutes
  • 1 psi = 2.31 feet of water; 1 foot of water = 0.433 psi
  • 0.785 = pi divided by 4; 8.34 = pounds per gallon

Pressure, head, and storage

  • Pressure to head: feet = psi × 2.31
  • Head to pressure: psi = feet × 0.433
  • Per-capita demand = total use in gallons per day ÷ population
  • Water loss percent = (produced minus billed) ÷ produced × 100
  • Tank volume in gallons = 0.785 × diameter squared × height × 7.48
  • Storage turnover = volume ÷ flow

Velocity and flow

  • Flow = area × velocity, where pipe area = 0.785 × diameter squared, diameter in feet
  • Velocity = flow ÷ area
  • Travel time = distance ÷ velocity

Wells

  • Drawdown = pumping level minus static level
  • Specific capacity = well yield in gallons per minute ÷ drawdown in feet

Disinfection and dosage

  • Pounds per day = concentration (mg/L) × flow (MGD) × 8.34
  • Dose = demand + residual
  • CT = residual (mg/L) × contact time (minutes)

Pumps and power

  • Water horsepower = (gallons per minute × head) ÷ 3,960
  • Brake horsepower = water horsepower ÷ pump efficiency
  • Motor horsepower = brake horsepower ÷ motor efficiency
  • Energy cost = horsepower × 0.746 × hours × cost per kilowatt-hour
  • Ohm's law: volts = amps × ohms; power = volts × amps

Use it

Keep this beside the water distribution math page, work the problems by hand, and check them in the operator calculator. Whether a calculator is allowed and the time limit are state-by-state, both listed on your state's page.

Wastewater treatment formula sheet

The reference, in our own notation, for the heaviest math track. The exam gives you a sheet like this one, closed book, so study it until the formulas are second nature. Each is taught on the wastewater treatment math page.

Conversions and constants

  • 1 cubic foot = 7.48 gallons; 1 gallon of water = 8.34 pounds
  • 1 MGD = 694 gallons per minute = 1.547 cubic feet per second
  • 1 percent = 10,000 mg/L; in water, mg/L equals ppm
  • 0.785 = pi divided by 4; 8.34 = pounds per gallon

Geometry, flow, and detention

  • Area of a circle = 0.785 × diameter squared
  • Volume of a cylinder in gallons = 0.785 × diameter squared × depth × 7.48
  • Flow = area × velocity; detention time = volume ÷ flow

Pounds, dosage, and loading

  • Pounds per day = concentration (mg/L) × flow (MGD) × 8.34
  • Organic loading = BOD (mg/L) × flow (MGD) × 8.34, in pounds per day
  • Surface overflow rate = flow in gallons per day ÷ surface area in square feet
  • Weir overflow rate = flow in gallons per day ÷ weir length in feet
  • Solids loading rate = pounds of solids per day ÷ surface area in square feet
  • Percent removal = (influent minus effluent) ÷ influent × 100

Activated-sludge process control

  • Food to microorganism ratio = pounds of BOD per day ÷ pounds of volatile solids under aeration
  • Pounds of volatile solids = volatile solids (mg/L) × aeration volume (MG) × 8.34
  • Mean cell residence time = pounds of solids in the system ÷ pounds of solids leaving per day
  • Sludge volume index = (30-minute settled mL/L ÷ solids mg/L) × 1,000
  • Percent volatile = volatile solids ÷ total solids × 100

Pumps, power, and lab

  • Water horsepower = (gallons per minute × head) ÷ 3,960
  • Brake horsepower = water horsepower ÷ pump efficiency; motor horsepower = brake horsepower ÷ motor efficiency
  • BOD = (initial DO minus final DO) × (bottle mL ÷ sample mL)

Use it

Pair this with the wastewater treatment math page, work the reverse problems by hand, and verify in the operator calculator. Your state's calculator and time rules are on your state's page.

Wastewater collection formula sheet

Plain-notation reference for the collection exam: pipes, slopes, velocities, and lift stations. The exam is closed book with a provided sheet, so learn where each formula lives. The teaching is on the wastewater collection math page.

Conversions and constants

  • 1 cubic foot = 7.48 gallons; 1 gallon of water = 8.34 pounds
  • 1 MGD = 694 gallons per minute = 1.547 cubic feet per second
  • 1 cubic foot per second = 448.8 gallons per minute
  • 0.785 = pi divided by 4; convert pipe diameter from inches to feet first, where 12 inches = 1 foot

Slope, velocity, and pipe

  • Slope percent = (drop in feet ÷ run in feet) × 100
  • Flow = area × velocity, where pipe area = 0.785 × diameter squared, diameter in feet
  • Velocity = flow ÷ area; the self-cleansing target is about 2 feet per second
  • Pipe volume in gallons = 0.785 × diameter squared × length × 7.48
  • Travel time = length ÷ velocity

Lift stations and wet wells

  • Wet-well volume in gallons = length × width × depth × 7.48
  • Pump capacity = volume pumped down ÷ time, with inflow isolated
  • Run time = working volume ÷ (pump rate minus inflow); fill time = working volume ÷ inflow
  • Cycle time = run time + fill time

Capacity and infiltration

  • Manning's equation: flow in cubic feet per second = (1.49 ÷ roughness) × area × hydraulic radius to the two-thirds power × slope to the one-half power
  • Infiltration and inflow = wet-weather flow minus dry-weather flow

Dosing

  • Pounds per day = concentration (mg/L) × flow (MGD) × 8.34, for odor and corrosion control

Use it

Work this alongside the wastewater collection math page, do the cycle-time and slope problems by hand, and check them in the operator calculator. Confirm your state's exam rules on your state's page.

A free resource from Ziptility. We make software for small water systems.