How this calculation works
Every drain removes a fraction of the current perfectly mixed tank. Refill restores the original volume with water at the entered source concentration; repeat in the supplied order.
Next concentration = current concentration × (1 − changed fraction) + source concentration × changed fractionA worked example
Starting at 100 with source concentration 10, successive 25%, 25% and 50% changes leave 77.5, 60.625 and 35.3125. A 100 L tank uses 100 L replacement water in total.
Good to know
Perfect-mixing arithmetic only, not aquarium-care, livestock or treatment advice. No safe target or change size is recommended. Production, decay, evaporation and changing tank volume are excluded.
Reference: OpenStax: concentration and dilution principles (opens in a new tab) ↗
Repeated fractions do not add into one removal
Two 25% changes remove a quarter of the mixture each time. The second drain includes replacement water from the first refill, so the process is not equivalent to removing 50% of the original water in one operation.
With zero source concentration, two such changes retain 0.75 × 0.75 = 56.25% of the starting concentration. Source concentration adds another contribution at every refill.
Source water sets a mixing limit
Repeated replacement approaches the source concentration when the same fractional process continues. It cannot dilute below that source level in this model. If the source is more concentrated, replacement raises the tank concentration instead.
The comparison target has no safety meaning here. It is simply a number you enter in the same concentration unit. The reported direction follows whether the starting value is above or below that target.
Count liters separately from concentration
Tank volume determines replacement-water use, but the fractional concentration sequence is unchanged if the whole tank is scaled up proportionally. This helps separate mixing mathematics from water purchasing or storage.
The graph includes every completed change and the initial state. The mass-flow figure summarizes the early steps; the table retains the complete entered sequence, up to one hundred changes.
Use the result with the next measurement
The RO water recovery and running cost calculator can describe product and reject volumes separately. Neither that volume balance nor this dilution model establishes whether replacement water is suitable for an aquarium.
Perfect-mixing arithmetic only, not aquarium-care, livestock or treatment advice. No safe target or change size is recommended. Production, decay, evaporation and changing tank volume are excluded.
A few questions, answered
Do two 25% changes equal one 50% change?
No, later drains remove some replacement water as well.
Can dilution cross below source concentration?
Not under this model without another mechanism.
Does the target mean a safe aquarium level?
No, it is an entered comparison value only.