Operator calculators
Twelve calculators for the numbers operators run on the job and on the exam. Each one shows the steps, not just the answer, and links to a lesson with worked examples and practice questions.
For instructional use. Results assume the standard conversion factors shown for each formula; actual field calculations may need chemical strength, density, and other adjustments.
Pounds Formula (lb/day)Convert a flow and a concentration in mg/L into pounds per day.
lb/day = flow (MGD) × concentration (mg/L) × 8.34 lb/gal
Calculator
Load
62.55 lb/day
- 1. 2.5 MGD × 3 mg/L × 8.34 = 62.55 lb/day
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Chlorine Dosage (mg/L)Find the dose in mg/L from a feed rate in pounds per day.
dose (mg/L) = feed rate (lb/day) ÷ [flow (MGD) × 8.34]
Calculator
Dose
2 mg/L
- 1. 3 MGD × 8.34 = 25.02
- 2. 50 lb/day ÷ 25.02 = 2 mg/L
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Chemical Feed Pump SettingFind the mL/min a metering pump must deliver for a target dose.
feed (mL/min) = [flow (MGD) × 1,000,000 gal × 3.785 L/gal × dose (mg/L)] ÷ [strength (mg/mL) × 1,440 min/day]
Calculator
Pump setting
262.8 mL/min
- 1. Chemical needed = 0.5 × 1,000,000 × 3.785 × 2 = 3,785,000 mg/day
- 2. Feed = 3,785,000 ÷ (10 × 1,440) = 262.8 mL/min
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Detention TimeDivide basin volume by flow to find how long water stays in the tank.
detention time (min) = volume (gal) ÷ flow (gpm)
Calculator
Detention time
300 min
- 1. 150,000 gal ÷ 500 gpm = 300 min
- 2. 300 min ÷ 60 = 5 hr
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Filter Loading RateDivide flow by filter surface area for gpm per square foot.
loading rate (gpm/ft²) = flow (gpm) ÷ filter area (ft²)
Calculator
Loading rate
2 gpm/ft²
- 1. 900 gpm ÷ 450 ft² = 2 gpm/ft²
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Percent Strength of a SolutionFind pounds of chemical in a tank of solution from its volume and percent strength.
lb chemical = volume (gal) × 8.34 lb/gal × (percent strength ÷ 100)
Calculator
Chemical
521.25 lb
- 1. 12.5% ÷ 100 = 0.125
- 2. 500 gal × 8.34 × 0.125 = 521.25 lb
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Dilution (C₁V₁ = C₂V₂)Find the diluted concentration when a solution is made up to a larger volume.
C₂ = (C₁ × V₁) ÷ V₂
Calculator
Final concentration
1,000 same unit as C₁
- 1. C₂ = (50,000 × 10) ÷ 500 = 1,000
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Surface Overflow RateDivide flow in gpd by a circular clarifier's surface area.
SOR (gpd/ft²) = flow (gpd) ÷ [0.785 × diameter² (ft²)], with flow (gpd) = MGD × 1,000,000
Calculator
Surface overflow rate
424.4 gpd/ft²
- 1. Area = π × 60² ÷ 4 = 2,827.4 ft²
- 2. 1.2 MGD × 1,000,000 = 1,200,000 gpd
- 3. 1,200,000 gpd ÷ 2,827.4 ft² = 424.4 gpd/ft²
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Wet Well Pumping RateFind a pump's rate from how fast the wet well level drops.
pumping rate (gpm) = [length (ft) × width (ft) × drop (ft) × 7.48 gal/ft³] ÷ time (min)
Calculator
Pumping rate
119.68 gpm
- 1. 8 × 8 × 2.5 = 160 ft³
- 2. 160 ft³ × 7.48 = 1,196.8 gal
- 3. 1,196.8 gal ÷ 10 min = 119.68 gpm
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Brake and Motor HorsepowerAccount for pump and motor efficiency to find the motor horsepower required.
motor hp = [flow (gpm) × head (ft) ÷ 3,960] ÷ pump efficiency ÷ motor efficiency
Calculator
Motor horsepower
33.67 hp
- 1. Water hp = 1,000 × 90 ÷ 3,960 = 22.73 hp
- 2. Brake hp = 22.73 ÷ 0.75 = 30.3 hp
- 3. Motor hp = 30.3 ÷ 0.9 = 33.67 hp
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Food-to-Microorganism (F/M) RatioCompare the BOD you feed each day to the biomass in the aeration tank.
F/M = [flow (MGD) × BOD (mg/L) × 8.34] ÷ [tank volume (MG) × MLVSS (mg/L) × 8.34]
Calculator
F/M ratio
0.25 lb BOD/day per lb MLVSS
- 1. Food = 4 × 180 × 8.34 = 6,004.8 lb BOD/day
- 2. Microorganisms = 1.2 × 2,400 × 8.34 = 24,019.2 lb MLVSS
- 3. F/M = 6,004.8 ÷ 24,019.2 = 0.25
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Mean Cell Residence Time (MCRT/SRT)Divide the solids in the system by the solids removed each day.
MCRT (days) = [MLSS (mg/L) × (aeration + clarifier volume, MG) × 8.34] ÷ [(WAS flow × WAS TSS + effluent flow × effluent TSS) × 8.34]
Calculator
MCRT
9.08 days
- 1. Solids in system = 2,500 × (1 + 0.25) × 8.34 = 26,063 lb
- 2. Solids removed = (0.04 × 8,000 + 2 × 12) × 8.34 = 2,869 lb/day
- 3. MCRT = 26,063 ÷ 2,869 = 9.08 days
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Looking for the rest? See all 25 math formulas.
Study guides
Understand the math behind the calculators
Water Operator Math Made Simple explains each formula step by step.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know