Formula and example
How it is calculated
C after = (C before + increase) × (1 − fraction replaced) + replacement concentration × fraction replaced. The increase is zero before the first change.
Worked example
100 l, 50 mg/l, 5 mg/l replacement water: after three 25% changes, 23.984375 mg/l, with no intermediate growth.
Things to check
- The calculation does not indicate a safe concentration and does not provide advice on fish care or water change frequency. Species, water parameters, and measurement reliability are separate issues.
- Use data for the same dissolved substance in the same mg/l unit. Plant uptake, decomposition, and regeneration are represented only by your own concentration increase between changes. Evaporation is not included in the model.
Frequently asked questions
Why isn't the removed fraction three times 25%?
On the second and third occasions, you also remove water previously added. With complete mixing, the proportion of original water is multiplied by 0.75 each time.
What does replacement water concentration mean?
The measured mg/l value of the same dissolved substance in the water being added. If this is higher than the value measured in the aquarium, the change may increase the calculated concentration.