Operator calculator
Dilution (C₁V₁ = C₂V₂) calculator
Find the diluted concentration when a solution is made up to a larger volume.
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.
Formula and inputs
C₂ = (C₁ × V₁) ÷ V₂
| Input | Unit |
|---|---|
| Starting concentration (C₁) | mg/L or % |
| Starting volume (V₁) | any volume unit |
| Final volume (V₂) | same unit as V₁ |
| Result: Final concentration | same unit as C₁ |
When to use it
Dilution keeps the amount of chemical the same while the volume grows, so concentration drops in proportion.
C₁V₁ = C₂V₂ works with any matching units. Just make sure both volumes use the same unit and both concentrations use the same unit.
Applies to: Water Treatment, Wastewater Treatment.
Exam tip: The answer must be smaller than the starting concentration. If it is larger, you flipped the volumes.
Study guides
Build the math skill behind the calculator
Water Operator Math Made Simple walks through the formulas step by step.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know