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California D3 water distribution exam math

In short

Exam size: the State Water Board's D3 exam has 100 questions across all subjects. Math questions are mixed in; the Board doesn't publish how many.
Math topics: 6 areas: unit conversions and pressure; area and volume; flow, velocity and detention; chemical feed and solutions; chlorination and CT; and wells, pumps and power.
Formulas: everything is solved with the Exam Conversion Sheet (revised 4/30/2026). D3 problems use 26 of its formulas, most often “Area of Circle = .785 X D2”, “Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48”, “Gas (lbs) = MG x mg/L x 8.34”.
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 D3 exam

What the State Water Board lists for D3 math

D1 - D5 Ability to convert water units
D1 - D5 Ability to convert units of volume, area, pressure, and time
D1 - D5 Ability to convert pressure to feet of head
D2 - D5 Ability to interpret SCADA information
D2 - D5 Ability to convert a pressure reading to depth of water
D1 - D5 Ability to calculate the area of a pipe cross-section
D1 - D5 Ability to calculate the volume of a well, storage reservoir, pipe, trench
D1 - D5 Ability to calculate the volume of a cylinder, rectangle, and square
D2 - D5 Ability to calculate the surface area of the interior walls of a storage reservoir
D1 - D5 Ability to calculate the surface area of a valve face
D2 - D5 Ability to calculate total force on a valve
D1 - D5 Ability to calculate flow rates
D2 - D5 Ability to calculate water velocity
D2 - D5 Ability to calculate pipe capacity
D3 - D5 Ability to calculate the cost of water production
D1 - D5 Ability to calculate a disinfectant dosage
D3 - D5 Ability to calculate CT
D2 - D5 Ability to calculate chlorine/ammonia ratio for chloramination
D1 - D5 Ability to calculate the well draw down
D3 - D5 Ability to calculate specific yield of a well
D3 - D5 Ability to calculate brake-horsepower
D3 - D5 Ability to calculate pump efficiency

Quoted from the SWRCB Expected Range of Knowledge, Drinking Water Distribution Exam (Rev. 4/2020). These are the objectives our D3 problems practice; the document lists every objective for the grade.

Conversion sheet formulas for D3

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

Area of Circle = .785 X D2124 problems
Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48100 problems
Gas (lbs) = MG x mg/L x 8.34100 problems
Specific Capacity (GPM/Ft) = Well Yield (GPM) / Drawdown (Ft)100 problems
HTH Solid (lbs) = MG x mg/L x 8.34 / (Strength (%)/100)50 problems
Liquid (Gal) = MG x mg/L x 8.34 / (Strength (%)/100 x Chemical Weight (lbs/gal))50 problems
Dosage (mg/L) = Demand (mg/L) + Residual (mg/L)50 problems
(Q) Flow (Ft3/Sec) = (A) Area (Ft2) x (V) Velocity (Ft/Sec)50 problems
mg/L = lbs / (MG x 8.34)50 problems
Area of Rectangle = Length x Width25 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
V (Ft/Sec) = Q (Ft3/Sec) / A (Ft2)25 problems
GPM = Volume (Gal) / Time (Min)25 problems
Process Units = (Live Signal (mA) - 4 mA) x Process Range / 16 mA25 problems
Cost/Day ($) = Lbs/Day x Cost/lb ($)25 problems
Water HP = GPM x Head (Ft) / 396025 problems
Brake HP = GPM x Head (Ft) / (3960 x (Pump % Eff/100))25 problems
Motor HP = GPM x Head (Ft) / (3960 x (Pump % Eff/100) x (Motor % Eff/100))25 problems
WWE (%) = (Pump % Eff/100) x (Motor % Eff/100)25 problems
lbs Force = PSI x Area (in2)25 problems
ppm or mg/L = lbs / (MG x 8.34)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

Free printable D3 worksheet

10 problems across the D3 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 D3 worksheet

Practice CA D3 Math free Try 5 problems without signing up

D3 exam math questions

How many questions are on the California D3 exam?

100, across all of the exam's subjects, according to the State Water Board's Expected Range of Knowledge for the distribution 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 D3 exam?

6 areas: unit conversions and pressure; area and volume; flow, velocity and detention; chemical feed and solutions; chlorination and CT; and wells, pumps and power. The Expected Range of Knowledge lists objectives such as the “ability to convert water units” and the “ability to calculate pump efficiency”.

Which formulas do I need for the D3 exam?

The ones on the State Water Board's Exam Conversion Sheet (revised 4/30/2026). The D3 problems here use 26 of its formulas; the most common are “Area of Circle = .785 X D2”, “Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48”, “Gas (lbs) = MG x mg/L x 8.34”. The conversion sheet page shows each formula with a worked example.

Is there a free D3 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 1,124 D3 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.