Estimate how much original water remains and the concentration of a dissolved substance after repeated drain-and-refill changes. Each change removes the same percentage of the aquarium’s water volume, then restores that volume. The model assumes perfect mixing before each removal, constant refill concentration, and no production, consumption or other removal of the substance between changes.
Enter a change size from 0 to 100%, and an integer count from 0 to 10,000. The count uses step 1; any fractional count passed through is rounded down to completed changes, and the count used is displayed. Enter both concentrations in mg/L for the same substance and reporting basis, within 0–1,000,000 mg/L. These are calculation bounds, not aquarium target ranges.
Use the percentage of actual water volume removed, including connected circulating water where applicable. Tank volume is unnecessary when the percentage is already known. Drain first, refill to the original volume, and allow complete mixing before the next change. Simultaneous draining and refilling is a different model.
Results are rounded for display. A very small positive fraction may display as zero; unavailable results do not mean zero.
Each change retains the fraction 1 − f of the water present immediately before it. Therefore R₀ = 1 and Rₖ₊₁ = (1 − f)Rₖ, giving Rₙ = (1 − f)ⁿ. Repeated partial-change dilution is illustrated in Wade Lehmann’s Short Take: Necessary Maintenance — Water Changes.
The constant-refill formula here follows directly from mass balance: Cₖ₊₁ = (1 − f)Cₖ + fCᵣ. Subtracting Cᵣ gives Cₖ₊₁ − Cᵣ = (1 − f)(Cₖ − Cᵣ), so the difference from refill concentration decreases by the same factor each time.
| Change size | Changes | Initial (mg/L) | Refill (mg/L) | Original-water fraction | Final concentration (mg/L) |
|---|---|---|---|---|---|
| 25% | 4 | 40 | 0 | 0.75⁴ = 0.31640625 | 0 + (40 − 0) × 0.31640625 = 12.65625 |
| 25% | 4 | 40 | 5 | 0.31640625 | 5 + (40 − 5) × 0.31640625 = 16.07421875 |
| 50% | 2 | 40 | 0 | 0.5² = 0.25 | 10 |
| 100% | 0 | 40 | 5 | 1 | 40 |
| 100% | 1 | 40 | 5 | 0 | 5 |
| 0% | 4 | 40 | 5 | 1 | 40 |
| 50% | 2 | 2 | 10 | 0.25 | 10 + (2 − 10) × 0.25 = 8 |
This is a dilution calculation for a conserved dissolved substance. It excludes ongoing production, biological uptake, chemical reactions, adsorption, evaporation, dosing and changes in refill concentration. It does not calculate pH, which is logarithmic. Real measured concentrations can differ when these assumptions do not hold.
If refill concentration exceeds the initial concentration, changes raise the concentration toward the refill value. The original-water fraction still decreases independently of that concentration trend. A mathematical 100% change is an endpoint of the model, not a recommended husbandry procedure.
Do four 25% changes replace all the original water?
No. They process a cumulative volume equal to the aquarium’s water volume, but later changes also remove some previously added water. After four changes, 31.640625% of the original water remains.
What happens with no changes?
The original-water fraction is 1 and concentration remains at the initial value, regardless of the entered change percentage.
Can this calculate changes with different percentages?
This calculator assumes the same percentage for every change. Different percentages require multiplying the individual retained fractions instead of using one repeated power.
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