Water operator math tutorial
Chlorine Dosage (mg/L)
Find the dose in mg/L from a feed rate in pounds per day.
Dosage questions run the pounds formula backwards: you know how much chlorine was fed and need the concentration it produced in the water.
Rearranging is the whole skill. Keep 8.34 in the denominator along with the flow.
The formula
dose (mg/L) = feed rate (lb/day) ÷ [flow (MGD) × 8.34]
| Variable | Unit |
|---|---|
| Feed rate | lb/day |
| Flow | MGD |
| Result: Dose | mg/L |
Conversion factors used: 8.34 lb per gallon of water.
Applies to: Water Treatment, Water Distribution.
Common exam tip: If the answer is under about 0.1 mg/L or over 10 mg/L for ordinary disinfection, recheck your units.
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.
Worked examples
Example 1
A chlorinator feeds 50 lb/day into a 3 MGD flow.
- 3 MGD × 8.34 = 25.02
- 50 lb/day ÷ 25.02 = 2 mg/L
Answer: 2 mg/L
Example 2
125 lb/day of chlorine is fed to a 6 MGD plant.
- 6 MGD × 8.34 = 50.04
- 125 lb/day ÷ 50.04 = 2.5 mg/L
Answer: 2.5 mg/L
Common mistakes
Wrong result: 16.67 mg/L
forgetting to include 8.34 in the denominator
Wrong result: 1,251 mg/L
multiplying instead of dividing
Practice questions
1. Feed is 18 lb/day at 1.2 MGD. What is the dose?
- A1.8 mg/L
- B15 mg/L
- C180.14 mg/L
- D18 mg/L
Show answer and explanation
Correct answer: A. 1.2 MGD × 8.34 = 10.008 18 lb/day ÷ 10.008 = 1.8 mg/L Answer: 1.8 mg/L. A common slip is forgetting to include 8.34 in the denominator, which gives 15 mg/L.
2. Feed is 240 lb/day at 8.5 MGD. What is the dose?
- A28.24 mg/L
- B3.39 mg/L
- C17,013.6 mg/L
- D33.9 mg/L
Show answer and explanation
Correct answer: B. 8.5 MGD × 8.34 = 70.89 240 lb/day ÷ 70.89 = 3.39 mg/L Answer: 3.39 mg/L. A common slip is forgetting to include 8.34 in the denominator, which gives 28.24 mg/L.
3. Feed is 9.5 lb/day at 0.45 MGD. What is the dose?
- A21.11 mg/L
- B35.65 mg/L
- C2.53 mg/L
- D25.3 mg/L
Show answer and explanation
Correct answer: C. 0.45 MGD × 8.34 = 3.753 9.5 lb/day ÷ 3.753 = 2.53 mg/L Answer: 2.53 mg/L. A common slip is forgetting to include 8.34 in the denominator, which gives 21.11 mg/L.
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Water Treatment
Water Distribution
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know