How to use the aquarium water change calculator
- Enter the current level from your test, such as nitrate in ppm, and the level in the replacement water. Tap water is often not zero, so test it.
- Enter the share of water changed each time and the number of changes you plan.
- Optionally enter a level you want to reach, and the tank volume to see how much water each change moves.
- Read the level after the planned changes, the table of every change and the number of changes needed for your target.
Formula
level after one change = source + (level - source) x (1 - fraction changed)
level after n changes = source + (start - source) x (1 - fraction)^n
changes needed = ln((target - source) / (start - source)) / ln(1 - fraction), rounded up
Each change replaces a fraction of the water with new water at the source level, so the gap between the tank and the source shrinks by a constant factor every time. The level can approach the source level but never go below it.
Bringing a level of 60 down with 25% changes
Start at 60 ppm with replacement water at 5 ppm and change 25% each time. After 1 change the level is 46.25. After 3 changes it is 5 + 55 x 0.75^3 = 28.2031, and after 5 changes it is 18.0518. To reach 20 ppm or less takes 5 changes. For a 40 liter tank, each change moves 10 liters.
A target at or below the replacement level can never be reached, because new water at 5 ppm keeps the tank above 5. Asking for 3 ppm in the example shows "not reachable" with a warning.
Why more, smaller changes are not the same as one big one
Replacing a share of the water is like repeated dilution. Two changes of 25% leave 0.75 x 0.75 = 56.25% of the original gap, not 50%, because the second change removes part of the already-diluted water. To remove more with fewer steps you need a larger share each time.
This is the same arithmetic as a serial dilution or a half-life decay. The Dilution and Molarity Calculator covers the lab version, and the Half-Life Calculator the decay version.
What the numbers do not tell you
The model assumes complete mixing and no waste being added between changes, and a real tank keeps adding waste, so the level rises again between changes. It describes dilution only. It does not say what level is safe for any animal or plant, and the target is yours to choose from reliable guidance for your species. For salt additions, see the Aquarium Salt Calculator, and for tank volumes the Tank Volume Calculator.
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Assumptions and limits
- New water mixes completely with the tank before the next change.
- Nothing is added to the tank between changes, and the substance does not break down or get used up.
- The replacement level is the same for every change.
- The level is any measurable substance in matching units, such as mg/L or ppm.
- The example levels are an illustration. Replace them with your own.
Frequently asked questions
How many changes does it take to remove most of a substance?
With 50% changes, each one halves the gap to the source level, so 3 changes remove 87.5% of the gap. Smaller changes need many more.
Why does the page not say what level is safe?
Safe levels depend on the animals and plants and on the substance, and they are not a single number. The page does the arithmetic only, so use guidance for your own species for any target.
What if my tap water has the same level as the tank?
Then changes cannot lower it at all. The level stays at the source level, and the page says the target cannot be reached. A different source of water or another method is needed.
Can I use percentages above 50%?
Yes, up to 100%. A 100% change replaces everything and brings the level straight to the replacement level in one step.