Operator math hub
Learn the formulas behind water and wastewater operator exams.
Math applies across treatment, distribution, wastewater, and collection exams. These tutorials use one repeatable format: formula, variables, worked examples, common mistakes, calculator, and practice questions.
25
formula tutorials
4
operator disciplines
75+
practice prompts
Start with these 10 core tutorials
8 tutorials
Beginner operator math
Core unit conversions, dosage, demand, detention time, volume, and percent removal.
Flow Unit Conversions (gpm to MGD)
Convert gallons per minute to million gallons per day.
Treatment · Distribution · Wastewater · Collection
Pounds Formula (lb/day)
Convert a flow and a concentration in mg/L into pounds per day.
Treatment · Distribution · Wastewater
Chlorine Dosage (mg/L)
Find the dose in mg/L from a feed rate in pounds per day.
Treatment · Distribution
Chlorine Demand and Residual
Subtract the residual from the dose to find the demand.
Treatment · Distribution
Detention Time
Divide basin volume by flow to find how long water stays in the tank.
Treatment · Distribution · Wastewater · Collection
Percent Removal
Express how much of a pollutant a process removes.
Treatment · Wastewater
Tank Volume in Gallons
Find the volume of a cylindrical tank from diameter and water depth.
Treatment · Distribution · Wastewater
Pipe Volume in Gallons
Find how many gallons a section of pipe holds.
Distribution · Collection
8 tutorials
Intermediate operator math
Hydraulics, filter rates, loading rates, dilution, chemical feed, and flow relationships.
Pressure and Head
Convert feet of head to pounds per square inch.
Distribution · Treatment
Flow, Velocity, and Area (Q = V × A)
Find flow in cfs from cross-sectional area and velocity.
Treatment · Distribution · Wastewater · Collection
Filter Loading Rate
Divide flow by filter surface area for gpm per square foot.
Treatment
Filter Backwash Rate
Find the backwash rate from the backwash flow and the filter dimensions.
Treatment
Weir Overflow Rate
Divide daily flow by weir length for gallons per day per foot.
Treatment · Wastewater
Surface Overflow Rate
Divide flow in gpd by a circular clarifier's surface area.
Treatment · Wastewater
Chemical Feed Pump Setting
Find the mL/min a metering pump must deliver for a target dose.
Treatment · Distribution
Dilution (C₁V₁ = C₂V₂)
Find the diluted concentration when a solution is made up to a larger volume.
Treatment · Wastewater
9 tutorials
Advanced process-control math
Horsepower, biological wastewater control, sludge metrics, CT, and lift station calculations.
Water Horsepower
Compute the power a pump delivers to the water from flow and head.
Treatment · Distribution · Wastewater · Collection
Brake and Motor Horsepower
Account for pump and motor efficiency to find the motor horsepower required.
Treatment · Distribution · Wastewater · Collection
Food-to-Microorganism (F/M) Ratio
Compare the BOD you feed each day to the biomass in the aeration tank.
Wastewater
Mean Cell Residence Time (MCRT/SRT)
Divide the solids in the system by the solids removed each day.
Wastewater
Sludge Age
Divide the solids in the aeration tank by the solids coming in each day.
Wastewater
Sludge Volume Index (SVI)
Relate 30-minute settled volume to MLSS to judge how well sludge settles.
Wastewater
Percent Strength of a Solution
Find pounds of chemical in a tank of solution from its volume and percent strength.
Treatment · Distribution · Wastewater
CT Calculation
Multiply the residual by contact time to get CT in mg·min/L.
Treatment
Wet Well Pumping Rate
Find a pump's rate from how fast the wet well level drops.
Collection · Wastewater
Study guides
Want the full math path in one guide?
Water Operator Math Made Simple organizes the same kind of exam math into step-by-step lessons, printable references, and a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know