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California T3 water treatment exam math

In short

Exam size: the State Water Board's T3 exam has 100 questions across all subjects. Math questions are mixed in; the Board doesn't publish how many.
Math topics: 7 areas: unit conversions and pressure; area and volume; flow, velocity and detention; chemical feed and solutions; chlorination and CT; wells, pumps and power; and filtration and removal.
Formulas: everything is solved with the Exam Conversion Sheet (revised 4/30/2026). T3 problems use 43 of its formulas, most often “Area of Rectangle = Length x Width”, “Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)”, “Area of Circle = .785 X D2”.
How to study: find each topic's formulas on the sheet, work the examples on the topic pages, practice one topic at a time until most answers come out right, then mix topics in timed sets.

Math topics on the T3 exam

What the State Water Board lists for T3 math

T1 - T4 Ability to convert common water units, (gallons per minute to MGD, etc…)
T1 - T4 Ability to convert units of length, volume, flow and pressure
T1 - T4 Ability to convert head pressure to water elevation
T1 - T4 Ability to calculate well head pressure
T1 - T4 Ability to read and interpret water meter readings
T2 - T4 Ability to analyze a water sample for water hardness
T1 - T4 Ability to calculate a chemical solution concentration
T1 - T4 Knowledge of basic SCADA system components
T1 - T4 Ability to determine water level in a storage tank, reservoir or well
T1 - T4 Ability to calculate flow rates and water velocity
T1 - T4 Ability to calculate the volume of water in a storage facility
T1 - T4 Ability to calculate detention time
T3 - T4 Knowledge of sedimentation basins
T2 - T4 Ability to calculate a dilution factor
T2 - T4 Ability to perform dilutions
T3 - T4 Ability to perform blending calculations
T1 - T4 Ability to calculate a dosage for a chemical feeder
T1 - T4 Ability to calculate a chemical dosage
T3 - T4 Ability to calculate a coagulant dose from a jar test
T3 - T4 Ability to calculate the cost of water treatment operations
T1 - T4 Ability to calculate chlorine demand and chlorine residual
T2 - T4 Ability to calculate a CT value
T1 - T4 Ability to calculate well drawdown
T1 - T4 Ability to calculate well specific capacity
T3 - T4 Ability to calculate a filtration rate
T3 - T4 Ability to calculate filter loading rate
T2 - T4 Ability to calculate daily filter production
T2 - T4 Ability to calculate filter backwash rate
T3 - T4 Ability to calculate percent or log removal of contaminants from water

Quoted from the SWRCB Expected Range of Knowledge, Drinking Water Treatment Exam (Rev. 4/2020). These are the objectives our T3 problems practice; the document lists every objective for the grade.

Conversion sheet formulas for T3

Most used first. Each links to a worked example on the conversion sheet page.

Area of Rectangle = Length x Width150 problems
Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)100 problems
Area of Circle = .785 X D299 problems
Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.4875 problems
Gas (lbs) = MG x mg/L x 8.3475 problems
HTH Solid (lbs) = MG x mg/L x 8.34 / (Strength (%)/100)50 problems
Dosage (mg/L) = Demand (mg/L) + Residual (mg/L)50 problems
mg/L = lbs / (MG x 8.34)50 problems
ppm or mg/L = lbs / (MG x 8.34)50 problems
Rectangular Basin (Gal) = Length (Ft) x Width (Ft) x Height (Ft) x 7.4825 problems
Circumference of a Circle = 3.14 x D25 problems
Liquid (Gal) = MG x mg/L x 8.34 / (Strength (%)/100 x Chemical Weight (lbs/gal))25 problems
(Q) Flow (Ft3/Sec) = (A) Area (Ft2) x (V) Velocity (Ft/Sec)25 problems
V (Ft/Sec) = Q (Ft3/Sec) / A (Ft2)25 problems
GPM = Volume (Gal) / Time (Min)25 problems
C1 x V1 = C2 x V225 problems
(C1 x V1) + (C2 x V2) = C3 x V325 problems
Process Units = (Live Signal (mA) - 4 mA) x Process Range / 16 mA25 problems
Cost/Day ($) = Lbs/Day x Cost/lb ($)25 problems
Removal (%) = (In - Out) / In x 10025 problems
(lbs) Chemical = SG x 8.34 x Solution (Gal) x Solution (%/100)25 problems
Specific Gravity (SG) = Chemical Weight (Lbs/Gal) / 8.3425 problems
Chemical in Solution (%) = Dry Chemical (Lbs) x 100 / Solution Total Weight (lbs)25 problems
GPD = MGD x mg/L x 8.34 / ((% purity/100) x Chemical Wt. (lbs/gal))25 problems
GPD = (Feed, ml/min. x 1,440 min/day) / (1,000 ml/L x 3.785 L/gal)25 problems
Cost ($) = HP x .746 x Operating Hours (hrs) x $/kWh25 problems
DT (Min) = Volume (Gal) / Flow (GPM)25 problems
DT (hrs) = Ft3 x 7.48 x 24 / Gal/Day25 problems
SLR (GPD/Ft2) = Total Flow (GPD) / Surface Area (Ft2)25 problems
Weir Overflow Rate (GPD/Ft) = Flow (GPD) / Weir Length (Ft)25 problems
Liquid (Gal) = MG x mg/L x 8.34 / (Commercial Purity (%)/100 x Ion Purity (%)/100 x Chemical Weight (Lbs/gal))25 problems
C x T = Chlorine Residual (mg/L) x Time (min)25 problems
Time (min) = C x T / Chlorine Residual (mg/L)25 problems
Inactivation Ratio = Actual C x T / Table 25 problems
C x T Calculated = T10 Value, min x Chlorine Residual (mg/L)25 problems
Log Removal = 1.0 - (% Removal/100) x Log Key x (-1)25 problems
Filtration Rate (GPM/Ft2) = Filter Production (GPD) / (Filter Area (Ft2) x 1440)25 problems
Loading Rate (GPM/Ft2) = Flow Rate (GPM) / Filter Area (Ft2)25 problems
Daily Filter Production (GPD) = Filter Area (Ft2) x (GPM/Ft2) x 144025 problems
Backwash Volume (Gal) = Filter Area (Ft2) x Backwash Rate (GPM/Ft2) x Time (min)25 problems
Backwash Rate (GPM/Ft2) = Flow Rate (GPM) / Filter Area (Ft2)25 problems
Rate of Rise (Inches/min) = Backwash Rate (GPM/Ft2) x 12 (in/Ft) / 7.48 (gal/Ft3)25 problems
Unit Filter Run Volume (UFRV) = Volume Produced in a Filter Run (Gal) / Filter Area (Ft2)25 problems

Free printable T3 worksheet

10 problems across the T3 topics, with room to work and an answer key on the last page. No sign-up; print it or save it as a PDF.

Open the T3 worksheet

Practice CA T3 Math free Try 5 problems without signing up

T3 exam math questions

How many questions are on the California T3 exam?

100, across all of the exam's subjects, according to the State Water Board's Expected Range of Knowledge for the treatment exam. Math questions are mixed in with the rest, and the Board does not publish how many there are. Check the State Water Board's operator certification page for current exam rules.

What math is on the T3 exam?

7 areas: unit conversions and pressure; area and volume; flow, velocity and detention; chemical feed and solutions; chlorination and CT; wells, pumps and power; and filtration and removal. The Expected Range of Knowledge lists objectives such as the “ability to convert common water units, (gallons per minute to MGD, etc…)” and the “ability to calculate percent or log removal of contaminants from water”.

Which formulas do I need for the T3 exam?

The ones on the State Water Board's Exam Conversion Sheet (revised 4/30/2026). The T3 problems here use 43 of its formulas; the most common are “Area of Rectangle = Length x Width”, “Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)”, “Area of Circle = .785 X D2”. The conversion sheet page shows each formula with a worked example.

Is there a free T3 practice test?

Yes. The worked examples on each topic page and the printable 10-problem worksheet with answer key are free without an account. A free account adds practice from all 1,424 T3 problems with worked solutions, and timed sets. It covers the math only, not the whole exam.

Formulas and constants: CA Exam Conversion Sheet (revised 4/30/2026). Exam rules and the full range of knowledge: State Water Board operator certification.

WaterExamMath is independent practice software. It is not affiliated with, endorsed by or connected to the California State Water Resources Control Board. It covers the math portion of the drinking water operator exams only, not the whole exam, and passing is not guaranteed. Practice problems by WaterExamMath.