# VI. Water Change Math

Water Change Math – General

In other articles I push using nitrate (NO3) as an indicator of general pollution, and I still do that, but obviously that cannot be used in a planted tank, or even in tanks with functional microporous biomedia – which can denitrify, or in tanks with plenums – which do denitrify, coil denitrators – also for denitrification, or with added chemicals or exchange materials which complex nitrate. So what do we use? We have nothing that we can measure directly by hobby level test kits. Instead we use a hand-held calculator, or the comparable program in our computers, or even by pencil and paper. We calculate what our water changes are doing and what they are leaving behind, and then we decide what sort of schedule we can live with and/or live up to, and then that is what we do.

First I need to digress just a bit more. Water changes are to me generally the best single technique you can use for your tanks. Filters, pumps, plants, lights, heaters, and many other devices are routinely and constantly employed in our tanks, but none will or can do everything that a simple, ordinary partial water change accomplishes.

The only warnings involved with water changes are two:

1) Water changes will not be harmful to your fish or tank so long as the general water parameters are fairly closely matched – this means temperature, general hardness (GH, calcium and magnesium ions), and alkalinity (KH, a.k.a. carbonate hardness, carbonate and bicarbonate ions). The total dissolved solids (TDS) of the tank or replacement water should not be too far apart either. Very few hobbyists have TDS meters, and likely even fewer use them routinely. We work around this by common sense. If you have nitrate titers at or above ~100ppm, the TDS is way off from that of tap water with a nitrate titer of 0-10ppm. You cannot do a large-scale change without risk of osmotic shock to the fish. In that same situation, the pH and KH of the tap (source water) is likely far higher than the tank as well. That tank is in OTS, or Old Tank Syndrome. That is a special case and is treated in separate notes {OTS, OTS Changes}. Similarly, if you have been treating by large salt addition (>1 teaspoon/gallon), or using commercial buffers (or similar materials) routinely, or RO (reverse osmosis water) or DI (deionized water) without significant added mineral supplement, then the TDS will not match closely with tap water. In these cases simply do smaller, more frequent smaller partials rather than the most efficient or effective larger scale partials. It is far better to avoid shocking the fish rather than to be most efficient for the water partial.

Water changes at large percentages will be helpful, possibly even life saving, to your fish in the case of unoxidized metabolites (ammonia and/or nitrite) in the water. The hazardous or toxic concentrations of ammonia and/or nitrite are so low that TDS change is tiny. This also will be handled separately for tanks with NTS, New Tank Syndrome {NTS}, or immature biofiltration and general tank microflora and microfauna.

Concepts of Dilutions and Residuals:

Everybody has the concept of dilution. You add water to tea or coffee or booze and it is made weaker, more dilute. This is part of what we do when we partial a tank. Other parts of partialling a tank may well involve vacuuming, rinsing filters, cleaning glass, etc., but for the water itself we remove some old water and then dilute the remainder with “cleaner”, less polluted, water – simple dilution. If the tank is one where we cannot use nitrate as a pollution indicator, we can only guess at pollution levels and set arbitrary water change schedules. We do know that dissolved minerals do not go away by themselves, nor do dissolved organics with any speed. Some minerals may be used up in normal operation – the carbonate/bicarbonate ions, which we measure as KH or alkalinity are such. They are used up by normal nitrification. So water changes can restore some minerals which have been used in normal tank operation and at the same time dilute other minerals which have increased from evaporation (water evaporates, minerals and organics stay behind) or been added with food and from its major end product, fish waste. So we all can easily see that we are diluting the remainder of the tank water when we do a water change.

A closely related concept is that of residuals. Residuals are the materials left in the old water when we dilute it. If we are working with a fish-only tank, no plants or other denitrification equipment or processes, we can easily use nitrate production and nitrate residual after changes to set the scale of our partials. If we have decided that we are comfortable with a baseline (the titer after the water change) of 10ppm nitrate (or 20, or 30ppm – these are arbitrary levels we select for ourselves to be our guideline), then fine. We can measure that. If our regular water changes result in ~10ppm after the change, or less, then we are happy. We can say that our change of some particular volume every so many days gives us that standard level of cleanliness which we have set for the tank. We can all figure out what percentage of the nominal volume (or of the measured fill volume) of the tank that water change represents simply by dividing the volume of the change by the volume of the tank. If it takes a 15 gallon change every week to keep a 50 gallon tank at our chosen level, then 15/50 = 0.3, or as a percentage, 30%. If the changes do not provide our selected baseline titer, then we need to do larger or more frequent water changes, or maybe both. When we have done that 30% partial water change, the residual water left from before the partial is 70%. That residual water held all the pollutants it had before the partial, but the addition of fresh water had diluted them. Now the titer of any given pollutant (nitrate or anything else dissolved in the water) should be reduced by at least the percentage of the partial water change. If the nitrate titer was 15 ppm before the change, then after the change it should be 15 ppm x 0.70 = ~10.5 ppm. Our test will at best read that as ~10 ppm residual nitrate and we are content. The same reduction will apply to anything dissolved in the tank which is not present in the make up water, whether we can test for it or not, and whether or not we even know it exists. Dilutions and residuals are general and non-discriminating. They apply across the board.

We tend to think of water changes by how much we change each time, and that is logical. That represents work effort from us. But if we do not have some handle to base our water change volume and schedule on, we may see what we need to do more easily if we think about residuals. Residuals are the other side of the same familiar coin. When we used the nitrate titer, we were using a residual. Without a titer to use we can still think about how much old water is left from before some arbitrary start time, with all pollutants included. In this note I’ll call that starting point simply “old water”, which really means residual water.

The tables I have set up are really simple, so don’t panic. Each column showing changes in the “old water” represents nothing more than the figure from the same column above it multiplied by the change percentage as a decimal. This is simple calculator entry, preserved as a table or grid so we can discuss it, and hopefully see it more easily. All these tables start with a “baseline” row, which would be the tank before any water change.

The first example, which shows large changes (50%) is short, so may be easiest to see:

50% Partials:

Change # Start % Old % Change End % Old
Baseline 100.00 none 100.00
1 100.00 50 100.00
2 50.00 50 25.00
3 25.00 50 12.50
4 12.50 50 6.25

The first column only shows the partials, first, second, etc. after the arbitrary start at “change #1”.

The second column shows the amount of original or old water before the change.

The third column shows the percentage changed, so stays constant at 50% for this grid.

The forth column shows the residual amount of “old water” – the original water left from before we started this sequence of changes.

Throughout this note, I am going to use “less than 10%” original water as a standard. You can see that the fourth water change reduced the residual old water to less than 10%. For our purposes, if these partials were done weekly, we would have reduced whatever original pollution was present at the start to less than 10% of its starting value in less than a month. This does ignore any new pollution that has developed in that month, but that pollution is being diluted out as well and at the same rate, just from a different starting date based on when it appeared. What it is saying as a bottom line, or as the take-home lesson from this grid and this practice, is that in 4 weeks we have replaced more than 90% of the water in the tank relative to the arbitrary starting date. Or in other words, we have at any and all times less than 10% residual dissolved pollution more than 4 weeks old. Keep that bottom line in mind as we look at other tables.

20% Partials:

Change # Start % Old % Partial End % Old
Baseline 100.00 none 100.00
1 100.00 20 80.00
2 80 20 64.00
3 64 20 51.20
4 51 20 40.96
5 41 20 32.77
6 33 20 26.21
7 26 20 20.97
8 21 20 16.78
9 17 20 13.42
10 13 20 10.74
11 11 20 8.59
12 9 20 6.87

This table is basically the same, only showing that with 20% partials, to reach the same end point of replacing >90% of the old water, we would have to do 11 each 20% partials, about two and a half months if done weekly.

I did not include the comparable grid for 10% partials, as it is exactly twice as long as the 20% partial grid, 22 weeks, or about five months to >90% new water from any arbitrary start time.

An interesting (to me anyway) sidebar could be that if those same 10% partials were done daily, then that same >90% water replacement from any arbitrary start time would occur at 22 days, one day over three weeks. That would be an even better clearance of old water than that from 50% weekly partials. These two cases (~3 and 4 weeks respectively) would have to be the best and second-best general cases presented in this note. Unfortunately in the real world, even 10% daily partials are unlikely without either automation or high personal labor commitment or dollar labor costs.

More grids are included at the end of this note, and my feelings will not be hurt if you want to scan them now, but I think that these first two, plus the (not shown) doubling of the 20% grid for the smaller 10% changes gives us enough to talk about briefly, and perhaps to think about at some length.

I want my water as clean as I can have it with realistic handling. Each of us has to set their own standards for that. Otherwise notes like this would not be needed. Someone could just say that you must do XY% changes every certain interval. But that sort of statement, although seen routinely on the web, is highly unrealistic. All tanks are not the same, and everyone’s involvement in the hobby and time available for tank work is not the same. So this boils down to a plea for personal honesty with yourself – how much can you do with and for your tanks, and how much time and effort are you willing to devote to the tanks?

Throughout these discussions on water changes, there is another required comment which is often completely ignored in comments seen on the boards. That comment involves folks doing a series of partials and adding the volumes changed each time – for example, someone will do a series of 4 changes, 25%of the water volume each time. They add these change volumes together and consider that they have changed 100% of the water. That is incorrect, simply and quite misleadingly wrong. You cannot add volumes changed each time to read the effect of any series of separate partials. You have to consider the residual water after each change. Water changes are dilutions, each must be considered separately. This is the biggest single cause of misunderstanding of what water changes really are doing, and not doing for our water quality. Glance back up to the grid of 50% partials presented earlier in this note – even partials at the 50% level have not changed 100% of the old water out, even after four such changes, but only 75% – nowhere near the 200% that simple addition of the change amounts would seem to imply. This leads too many hobbyists to misunderstand how much they have improved, or not improved, the water quality by our repeated water changes.

To me, 5 months to replace >90% is massively excessive. Riverine fish (those living in flowing water) in the wild are accustomed to multiple total water changes per day, if not per hour. Lake dwelling fish live in many times larger volumes of water per fish than we provide – that is commonly much more per fish than we have in the whole tank. Estuary dwelling fish live in something between a river and effectively infinite water volume. Reef fish do live in effectively infinite water. We really should be able to do a lot better than 5 months for a 90% replacement, or even than 6 weeks for the same result. Do remember that the more frequently you do water changes, and the larger those changes are as a percentage of the tanks volume, the closer the tank water will stay to the source water, and the lower the residual pollution levels will be. But you have to make up your own mind and set your own schedule.

My personal schedule is based on weekly partials, from 33% (1/3), to 50% (1/2), depending on the stocking level and nature of the fish in each tank.

More grids with % partials:

25% Partials:

Change # Start % Old % Change End % Old
Baseline 100.00 none 100.00
1 100.00 25 75.00
2 75 25 56.25
3 56 25 42.19
4 42 25 31.64
5 32 25 23.73
6 24 25 17.80
7 18 25 13.35
8 13 25 10.01
9 10 25 7.51

At this level, >90% removal of old water is at 8 weeks, so just under two months.

33% (or 1/3) Partials:

Change # Start % Old % Change End % Old
Baseline 100.00 none 100.00
1 100.00 33 66.66
2 67 33 44.44
3 44 33 29.62
4 30 33 19.74
5 20 33 13.16
6 13 33 8.73

Here the >90% removal occurs at 6 weeks, just below a month and a half. I use this level myself for well-planted low to very low stocking density (read as low bioload) tanks.

One other key point is that we must not consider our tank water to be a copy, a duplication of the fish’s native water. It generally is not at all. For most but not all fish, our tank water is what we can provide conveniently and practically with only the most minor modifications. In the cases of most captive-bred fish, the closer our tank water is to our source water (what we get from our taps), the better and more easily and cheaply we can provide clean and healthy water for our captive fish. We only rarely need or try to match the true “wild” conditions of the fish. The commonest exception is for breeding of rainforest blackwater fish. Some of those creatures have egg membranes which are highly sensitive to calcium and/or magnesium ions (Ca++ and/or Mg++). Those ions, which we measure as GH (General Hardness), are damaging to the egg membranes of some of these fish. The effect is to tan or harden the egg membrane, which blocks either the penetration of the egg by sperm, or to toughen the membrane around the developing embryo such that it cannot break out of the egg. The nest effect is failure to reproduce. For those fish we must have reduced to very low levels of those particular ions if we wish to breed them. That generally require at least high rejection reverse osmosis water, supplemented with sufficient other ions to make it manageable in our tanks. But please do note that such water is required only during conditioning and breeding, not full-time and almost never in mixed tanks. Some few of these fish may show best color in relatively “soft” (low GH) water, but do not require the same water for maintenance that they need for reproduction. Artificial “blackwater” is extremely difficult to maintain in captivity. It cannot be supported by our usual tank techniques. Marine conditions for delicate inverts and some few fish may similarly need or operate best in captivity with artificial marine mixes supplement for a number of ions. These special exceptions are significantly more expensive to make up and difficult to operate than the large majority of hobbyists tanks, and thus are outside the scope of this article.

This article originally appeared in AquaSource Magazine. It has been edited and expanded for this site. July, 2011

Robert T. Ricketts, a.k.a RTR