Water Operator Exam Math: Key Formulas

Math scares many operators more than any other part of the exam. Yet most of it comes down to a dozen formulas and a few conversion factors.

The State Water Board hands you a formula sheet in the exam room, so you do not have to memorize everything. You do have to know which formula to pick and how to use it quickly.

This guide covers the formulas that show up again and again, with four worked examples. This site is an independent exam trainer. Certificates are issued by the State Water Board, not by us, and we are not affiliated with the Board or Prometric.

What the sheet gives you

Drinking water examinees receive the Board's Equivalents and Formula sheet, plus a built-in calculator and scratch paper or a dry erase board.² Distribution has its own sheet version with the same core formulas.³

Wastewater examinees get a different pair of sheets, and the Board says they receive both versions.² The wastewater sheet rounds some factors differently, for example 0.43 psi per foot instead of 0.433.⁴ Always use the numbers on the sheet in front of you.

The examples below are our own practice problems, not exam questions.

Volume and flow

The sheet gives the volume of a rectangular basin in gallons as length x width x height x 7.48 gallons per cubic foot. For a cylinder it uses 0.785 x diameter squared x height x 7.48.¹

Flow in a pipe follows Q = A x V: flow in cubic feet per second equals area in square feet times velocity in feet per second. Pipe area is 0.785 x diameter squared.¹

Example 1: basin volume

A sedimentation basin is 100 ft long, 30 ft wide and 12 ft deep. How many gallons does it hold?

Volume = 100 x 30 x 12 = 36,000 cubic feet. Then 36,000 x 7.48 = 269,280 gallons.

Detention time

Detention time is volume divided by flow. The sheet also gives a combined form: volume in cubic feet x 7.48 x 24 hours per day, divided by gallons per day.¹

Keep your units matched. If volume is in gallons and flow is in gallons per day, the answer is in days. Multiply by 24 for hours.

Example 2: detention time

The basin from Example 1 receives 3 MGD (3,000,000 gallons per day). What is the detention time?

269,280 gal / 3,000,000 gal/day = 0.0898 day. Then 0.0898 x 24 = 2.15 hours.

Chlorine dose

Two lines on the sheet do most of the work. First, dosage in mg/L equals demand plus residual.¹ Second, pounds of chlorine gas equal volume in million gallons x mg/L x 8.34 pounds per gallon.¹

The 8.34 is the weight of one gallon of water in pounds.¹ The same pattern gives pounds per day when you use MGD as the flow.

For a solid such as HTH, the sheet divides by the percent strength in decimal form. For example, 65 percent strength means dividing by 0.65.¹

Example 3: pounds per day

A plant treats 2.5 MGD. The chlorine demand is 1.8 mg/L and the target residual is 0.7 mg/L. How many pounds per day of chlorine gas are needed? How many pounds of 65 percent HTH?

Dose = 1.8 + 0.7 = 2.5 mg/L.

Gas = 2.5 MGD x 2.5 mg/L x 8.34 = 52.1 lb/day.

HTH = 52.1 / 0.65 = 80.2 lb/day.

Pressure and head

The sheet gives two equivalent routes. Pressure in psi equals head in feet divided by 2.31, or head in feet x 0.433.¹ To go the other way, multiply psi by 2.31 to get feet of head.

Example 4: pressure from a tank

The water surface in an elevated tank is 85 ft above a pressure gauge. What pressure does the gauge show?

85 x 0.433 = 36.8 psi. Check: 85 / 2.31 = 36.8 psi.

In reverse, a gauge reading 50 psi means 50 x 2.31 = 115.5 ft of head.

Unit conversions

Many errors are conversion errors. These come straight from the sheet.¹

Item	Value
1 cubic foot of water	7.48 gallons
1 gallon of water	8.34 pounds
1 mg/L	1 ppm
1 percent	10,000 mg/L
1 day	1,440 minutes or 86,400 seconds
1 MGD	1.55 cubic feet per second
1 acre	43,560 square feet
1 gallon	3.785 liters

To convert gallons per minute to MGD, multiply by 1,440 minutes per day and divide by 1,000,000. So 1,400 gpm is about 2.02 MGD.

Habits that save points

• Write the formula first, then the numbers, with units next to each.
• Convert flow and volume to matching units before you divide.
• Estimate the answer. A basin that holds under a day of flow cannot have a detention time of 30 hours.
• Round only at the end.
• Read what the question asks for: pounds per day, gallons per day or mg/L.

Wastewater adds its own formulas, such as BOD or suspended solids in pounds per day equal to 8.34 x flow in MGD x concentration in mg/L.⁴ Ten wastewater questions are math problems worth 4 points each.⁵

Ready to test yourself? Start a practice test, or Start a practice test for distribution, or Start a practice test for wastewater. For the exam formats, see the three exams compared. For the application steps, see the treatment certification guide.

Common questions

Do I need to memorize the formulas?

The Board provides a formula sheet at the test center.² You still need to practice, because time is limited and picking the right formula is the skill being tested.

Which value of 8.34 or 0.433 should I use?

Use the one on your sheet. Both treatment and distribution sheets list 8.34 pounds per gallon and 0.433 psi per foot.¹³

Is there a calculator on the exam?

Yes, a calculator is built into the exam software.²

Sources

Formulas and conversion factors come from the State Water Board's official sheets. The worked examples are our own calculations using those formulas.

1. State Water Board: Equivalents and Formula Sheet for Drinking Water Treatment Exams (waterboards.ca.gov)
2. State Water Board: Operator Certification Computer-Based Testing FAQs (waterboards.ca.gov)
3. State Water Board: Equivalents and Formula Sheet for Drinking Water Distribution Exams (waterboards.ca.gov)
4. State Water Board: Wastewater Operator Certification Equivalents and Formulae Sheet (rev. Jan 2014) (waterboards.ca.gov)
5. State Water Board: Grade I WWTP Operator Examination Information (waterboards.ca.gov)