Water operator math tutorial
Chlorine Demand and Residual
Subtract the residual from the dose to find the demand.
Chlorine demand is what the water consumed. Residual is what is left to keep disinfecting. The dose is the sum of the two.
Exam questions usually give two of the three values. Rearrange the same line to find the missing one.
The formula
demand (mg/L) = dose (mg/L) − residual (mg/L)
| Variable | Unit |
|---|---|
| Chlorine dose | mg/L |
| Chlorine residual | mg/L |
| Result: Demand | mg/L |
Applies to: Water Treatment, Water Distribution.
Common exam tip: Demand can never be negative. If you get a negative number you subtracted in the wrong order.
Calculator
Demand
2.4 mg/L
- 1. 3.2 mg/L − 0.8 mg/L = 2.4 mg/L demand
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
The dose is 3.2 mg/L and the residual is 0.8 mg/L.
- 3.2 mg/L − 0.8 mg/L = 2.4 mg/L demand
Answer: 2.4 mg/L
Example 2
A 5.5 mg/L dose leaves a 1.2 mg/L residual.
- 5.5 mg/L − 1.2 mg/L = 4.3 mg/L demand
Answer: 4.3 mg/L
Common mistakes
Wrong result: 4 mg/L
adding the residual instead of subtracting it
Wrong result: 0.25 mg/L
dividing instead of subtracting
Practice questions
1. Dose is 2.8 mg/L and residual is 0.6 mg/L. What is the demand?
- A2.2 mg/L
- B3.4 mg/L
- C0.21 mg/L
- D22 mg/L
Show answer and explanation
Correct answer: A. 2.8 mg/L − 0.6 mg/L = 2.2 mg/L demand Answer: 2.2 mg/L. A common slip is adding the residual instead of subtracting it, which gives 3.4 mg/L.
2. Dose is 4.1 mg/L and residual is 1.0 mg/L. What is the demand?
- A5.1 mg/L
- B3.1 mg/L
- C0.24 mg/L
- D31 mg/L
Show answer and explanation
Correct answer: B. 4.1 mg/L − 1 mg/L = 3.1 mg/L demand Answer: 3.1 mg/L. A common slip is adding the residual instead of subtracting it, which gives 5.1 mg/L.
3. Dose is 6.0 mg/L and residual is 1.5 mg/L. What is the demand?
- A7.5 mg/L
- B0.25 mg/L
- C4.5 mg/L
- D45 mg/L
Show answer and explanation
Correct answer: C. 6 mg/L − 1.5 mg/L = 4.5 mg/L demand Answer: 4.5 mg/L. A common slip is adding the residual instead of subtracting it, which gives 7.5 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