Water change dilution calculator
Partial water changes dilute geometrically. Several small changes remove much less than one large one of the same total volume.
ppm
ppm
%
ppm
ppm
Water changes needed
4.51
- Concentration after one change
- 57.50 ppm
- Single change that would do it
- 80.0 %
- Steady-state level at this schedule
- 40.00 ppm
- Total water used
- 271
- Water per change
- 60.0
- Target is above the tap water level
- 1
Show the working
- Tank volume = 200
- Current concentration = 80
- Target concentration = 20
- Change size = 30
- Level in the tap water = 5
- Produced per week = 15
- f = 30 / 100 = 0.3
- Concentration after one change = 80 * (1 - 0.3) + 5 * 0.3 = 57.5
- floor_level = 5 = 5
- Target is above the tap water level = 20 > 5 ? 1 : 0 = 1
- Water changes needed = (80 - 5) > 0 && (20 - 5) > 0 ? log((20 - 5)/(80 - 5), 1 - 0.3) : 0 = 4.512 34
- Single change that would do it = (80 - 5) > 0 ? (1 - (20 - 5)/(80 - 5)) * 100 : 0 = 80
- Total water used = 4.512 34 * 200 * 0.3 = 270.74
- Steady-state level at this schedule = 0.3 > 0 ? 5 + 15 * (1 - 0.3) / 0.3 : 0 = 40
- Water per change = 200 * 0.3 = 60
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- after one change: C x (1 - f) + source x f
- changes needed = log((target - source)/(current - source)) / log(1 - f)
You can never get below the level in your source water by changing water. That is the floor.
Three 20% changes remove 49% of a contaminant; one 60% change removes 60%. Bigger changes are more efficient.