ScapeMath

Water change & dilution calculator

Any parameter that water changes dilute (nitrate, phosphate, TDS, salinity, KH or a medication) follows the same simple mixing maths. Use whatever unit your test kit reads, as long as it's the same in every box.

ppm
ppm
%
L
Level afterwards
–
Water per change
–

Labels like "ppm" and "dKH" are only examples. The maths works in any unit if you use the same one throughout.

How it works

Removing a fraction f of the water takes away that fraction of whatever is dissolved in it. Refilling with new water adds that water's own level back. This is a simple mass balance:

After one change: C₁ = C·(1 − f) + C_new·f After n changes: Cₙ = C_new + (C − C_new)·(1 − f)ⁿ Change to hit target: f = (C − C_target) / (C − C_new) Blend of A and B: share of A = (B − target) / (B − A)

Two practical results follow. First, you can't get below your new water's level by changing water, however much you change. With 5 ppm nitrate tap water, 5 ppm is the floor. Second, several small changes are less efficient than one big one at removing a pollutant: two 25% changes leave 56% of it (0.75²), while one 50% change leaves 50%. On the other hand, small changes swing temperature, salinity and pH less, which is why many keepers still prefer them.

Worked examples

Nitrate after a 30% change

Tank at 40 ppm, tap at 5 ppm: 40 × 0.7 + 5 × 0.3 = 29.5 ppm. In a 100 L tank that means swapping 30 L. In a 26.4 US gal tank (100 L), it's 7.9 US gal.

How big a change gets you from 40 to 20 ppm?

(40 − 20) / (40 − 5) = 0.571, so a 57% change. With your usual 25% changes you'd need 3: 40 → 31.25 → 24.7 → 19.8 ppm.

Mixing RO and tap water to 4 dKH

RO at 0 dKH, tap at 12 dKH: share of RO = (12 − 4) / (12 − 0) = 2/3. For a 20 L bucket that's 13.3 L RO + 6.7 L tap. This works for GH, TDS and conductivity too, as long as they mix in a straight line, which dissolved salts do.

Limits

References

  1. Mass balance for completely mixed batch systems, e.g. Davis, M.L. (2010) Water and Wastewater Engineering, McGraw-Hill (mixing and dilution chapter)
  2. US EPA, Nitrate in drinking water (tap water can contain nitrate; Canada and the US set a 10 mg/L nitrate-N limit, ~45 mg/L as NO₃)
  3. Health Canada, Guidelines for Canadian Drinking Water Quality: Nitrate and Nitrite

Formulas on this page are checked by automated unit tests against the reference values above. Last reviewed October 29, 2026. Found an error? Tell us.

More calculators