Water Change Math
Water changes are often discussed in general terms in “Ask Jack.” One of this month’s
questions gives us an opportunity to put some actual numbers behind a discussion of water
changes. Don’t worry, you won’t need a calculator, but you may be surprised by what a
little math can reveal about aquarium husbandry.
Jack responds to a reader’s question this month by saying that he needs to know the
size of the tanks involved, not just the water change schedules. This is because water
change information alone will not tell you how fresh the water in an aquarium will
remain. A certain percentage water change necessarily involves the size of the aquarium.
For example, a 40-percent change on a 10-gallon tank brings in 4 gallons of fresh water,
while a 10-percent change on a 40-gallon tank brings in the same amount of fresh water, 4
gallons. The most significant figure to deal with when comparing water-change regimens
is the total amount of fresh water a tank receives in a given time period, so you need to
know the volume of the aquarium as well as the water-change regimen.
Is a larger tank always better? Jack has regularly told of his experiment splitting a
brood of discus fry and keeping one group in a small fish bowl, whose water was changed
many times a day, and the other in a larger tank that got a single daily change. For ease of
calculation, let’s say one tank is 2 gallons, the other 20. If all of the water in the small tank
is changed 10 times daily, the fish have 20 gallons of fresh water every day. If the larger
tank gets a 50-percent change once a day, that is only 10 gallons of fresh water every day.
While the volume the fish have to swim in does matter, the freshness of the water—which
is equivalent to the dilution of pollutants—is more important.
In the reader’s question, one tank (volume unspecified) gets 40 percent changed two to
three times per week, while the other (volume unspecified) gets 30 percent once a week.
Let’s assume that the tanks are the same size, say 40 gallons. Three 40-percent changes
give four times the volume as one 30-percent change, so with two 40-gallon tanks we have
fresh water volumes of 48 and 12 gallons per week.
Assume we can somehow identify how long a molecule of water has been in an
aquarium. When the two aquaria start out, there are 40 gallons of fresh water in each.
Since each change in the first tank removes 40 percent of all the water, we can assume it
removes 40 percent of each of the ages of water in the tank. So, after the first change there
are 16 gallons of fresh water and 24 gallons of old water. After the next change there are
again 16 gallons of fresh water, plus still 9. 6 gallons of the original water, and 14. 4 of
the water from the previous change. After the next change there are the 16 fresh gallons,
3. 8 gallons of the original water, 5. 8 of the water from the first change, and 14. 4 gallons
from the latest change. In the second aquarium in this time period there has only been one
change, so there are 12 gallons of fresh water and 28 gallons of old water. This is much
easier to see in a table:
(three water changes/week)
Fresh Old Older Oldest
14. 4 9. 6
14. 4 5. 8
16 3. 8
(one water change/week)
With frequent, large changes, there is a much greater volume of fresh water at any
given time, but this also means there is a rapidly diminishing amount of old water, which
is equally important when figuring the level of toxins to which the fish in that water are
Give your fish a mathematical advantage, and change more water, more often.