Chemical Analysis

Water Change Calculator

Calculate the number of changes requred to halve the pollutant concentration, whatever that might be.

Volume of Water :
Volume of Water Removed :

My dad (he is an Chemistry graduate so understands it all a lot better than me) put together this system calculate the volume of water which would neet changing.

SymbolDescription
aVolume of water in aquarium (litre)
bVolume of water removed in bucket (litre)
cConcentration of contaminant (e.g. nitrate) in solution at the start
nNumber of steps

If we siphon off b litres of liquid from the aquarium, and replace this volume with b litres of clean water, the concentration of material in solution will be: (a-b)c / a

e.g. If our aquarium holds 360 litres, and the bucket has a capacity of 10 litres, then replacing the first 10l of water will reduce the concentration of contaminant by a factor of (360 10)/360. i.e. 0.9722

After two steps, the contaminant will be reduced by 0.9722 x 0.9722. i.e. 0.9452

After three steps, the contaminant will be reduced by 0.9722 x 0.9722 x 0.9722. i.e. 0.97223 or 0.9189.

After n steps, the contaminant will be reduced by a factor 0.9722n.

To find out how many steps it will take to halve the concentration of contaminant, we need to solve the following mathematical equation:

0.9722n = 0.5
n log 0.9722 = log 0.5
n = log 0.5 / log 0.9722
n = 24.6

Rounding up to a whole number, we arrive at 25 steps.

To conclude, using a 10 litre bucket on a 360 litre aquarium, we must replenish the volume that we remove 25 times to halve the concentration of a contaminant, such as nitrate.

Fish are able to tolerate the slow reduction in concentration in a large number of small steps. Removing and replacing half the water in an aquarium in one step would be too much of a shock to them.

The table below shows what percentage of the original concentration of contaminant is left after each step to empty and replenish.

StepConcentration
197 %
295 %
392 %
489 %
587 %
684 %
782 %
880 %
978 %
1075 %
1173 %
1271 %
1369 %
1467 %
1566 %
1664 %
1762 %
1860 %
1959 %
2057 %
2155 %
2254 %
2352 %
2451 %
2549 %