Water change calculator: dilution, targets and steady state
Short answer
After a change of a fraction f of the water, the level is old × (1 − f) + new water × f: a 50 % change takes 40 mg/L down to 20 mg/L with pure water. If you add D mg/L a week and change a fraction f once a week, the level settles at a peak of D ÷ f just before each change, which is why EI's 50 % weekly change caps build-up at twice the weekly dose [1].
Three questions, one equation
A water change replaces a fraction of the tank water with new water, so the new concentration is a weighted average:
after = before × (1 − f) + new water × f
The calculator uses that line to answer three questions at once: what one change of your chosen size does, what single change would reach a target, and how many changes of your chosen size it takes. It works for any dissolved quantity measured the same way in both waters: nitrate, phosphate, potassium, a TDS reading or conductivity.
Repeated changes
Successive changes multiply. After n changes of fraction f, the difference between the tank and the new water shrinks to (1 − f)ⁿ of what it was. Three 30 % changes leave 0.7³ = 34 % of the original excess; a single 66 % change does the same with less new water (66 % of the tank volume instead of 90 %).
Dosing between changes: the steady state
If you add a fixed amount D (in mg/L) during each week and change a fraction f at the end of the week, the level climbs for a few weeks and then settles into a repeating pattern. At that point each change removes exactly what the week added:
peak (just before the change) = new water + D ÷ f trough (just after the change) = new water + D × (1 − f) ÷ f
With pure new water and a 50 % weekly change, the peak is twice the weekly dose. EI’s author describes exactly that ceiling: “a maximum of 2x the dosing they add per week” with 50 % weekly changes [1]. The EI Light write-up gives the same arithmetic for other change sizes: 10 ppm of nitrate a week peaks at about 12 ppm with a 90 % weekly change and about 40 ppm with a 25 % change [2]. The formula gives 11.1 and 40 ppm.
The calculator draws eight weeks of peaks and troughs from your current level, so you can see how quickly the pattern settles.
Worked example
Tank at 40 mg/L nitrate, tap water at 5 mg/L, 50 % change:
- One change: 40 × 0.5 + 5 × 0.5 = 22.5 mg/L.
- To reach 20 mg/L in one change: (40 − 20) ÷ (40 − 5) = 57 %.
- With 50 % changes: two changes (22.5, then 13.75 mg/L).
- Dosing 10 mg/L a week afterward: the peak settles at 5 + 10 ÷ 0.5 = 25 mg/L and the trough at 15 mg/L.
How big should changes be?
Sources differ, because they aim at different things. Tropica’s general care advice is to change about 25 % of the water every week [4]. EI prescribes 50 % a week as part of the dosing method, and allows more [1]. The PPS author argues that well-planted tanks with reasonable fish loads can run with fewer changes, and that the factor that drifts fastest in a given tank should set the minimum change rate [3]. The calculator does not pick a side; it shows what each choice does to the numbers.
Limits
- Uptake by plants, release from substrate and fish waste are not modeled.
- The new water’s level is taken as constant. Tap water quality can change seasonally.
- The steady-state formulas assume one change at the same point each week and an even weekly dose.
Questions
Why can't I reach my target with water changes?
Water changes can only bring the tank toward the level in the new water. If your tap water already has more nitrate than your target, no number of changes gets below that level; the calculator says so.
Is it better to do one big change or two small ones?
Two changes of 25 % leave 0.75 × 0.75 = 56 % of the old water, while one 50 % change leaves 50 %. The single large change removes slightly more, for the same amount of new water.
Does this include what plants take up?
No. The steady-state figures assume zero uptake, so they are ceilings. EI's author makes the same point: the maximum build-up applies when no uptake takes place [2].
Other calculators
- Dry fertilizer dosingConvert grams of KNO3, KH2PO4, K2SO4, Epsom salt or a trace mix into mg/L for your tank, or work back from a target ppm. Every molar mass is shown.
- EI and PPS-Pro plannerTurn the Estimative Index and PPS-Pro, as their authors published them, into grams or milliliters for your tank, with the build-up each schedule produces.
Background reading
- FertilizersEstimative Index (EI) dosing: what the method prescribesEI as Tom Barr wrote it up: dose a surplus three times a week, change 50 % of the water weekly, and why that caps build-up at twice the weekly dose.
- FertilizersNitrogen, phosphorus and potassium in planted tanksWhat N, P and K do in plants, the forms plants take up, how aquarium dosing expresses them, and what growers and dosing methods say about each.
- FertilizersPPS-Pro: the lean daily dosing method and its targetsPPS-Pro as its author published it: two 500 mL bottles, 1 mL per 40 L a day, low water-column targets, and how it differs from EI in intent and arithmetic.
Sources
- The Estimative Index of Dosing, or No Need for Test Kits. Tom Barr, The Barr Report (2005). A 50 % weekly change limits build-up to 2× the weekly dose; a 75 % change resets 75 % of the water. Accessed October 12, 2026.
- EI Light for those less techy folks. John N. and Tom Barr, The Barr Report. Worked numbers: 10 ppm NO3 a week peaks at 20 ppm with 50 % weekly changes, about 12 ppm with 90 %, about 40 ppm with 25 %, with no uptake. Accessed October 12, 2026.
- Water Changes. Edward, Perpetual Preservation System. The PPS author's view that well-run, fully planted tanks need fewer water changes; finding the factor that drifts sets the minimum change rate. Accessed October 12, 2026.
- Care. Tropica Aquarium Plants. Changing about 25 % of the water every week as general maintenance. Accessed October 12, 2026.