I tried searching the forums but I haven't found anything similar so I thought I would post it. This is just a simple formula with an explanation on how the calculation works.

Lets say you do Waterchanges at regular intervals (could be weekly, every 3 days, etc) and let X be the percentage water change you perform expressed in decimals. Meaning a 50% water change gives X=0.5. 40% WC gives X=0.4 and so on. Now given your current EI dosing scheme calculate how much of an element you are adding in between successive water changes. Call this Y.

Lets say you add 4ppm NO3 every day, and do weekly 50% water changes. Then X=0.50 and Y=4x7=28 (4 ppm over 7 days equals 28ppm). To calculate what level your NO3 value will plateau off at (making the simplifying assumption of zero uptake by plants...ie a worst case scenario) this is how your NO3 levels will look.

Week 1: Y

Week 2: Y+(1-X)Y

Note: (1-X) is the fraction of elements remaining in the tank after doing the waterchange.

Week 3: Y+(1-X)Y+((1-X)^2)Y

...

Week N: Yx(1+(1-X)+(1-X)^2+(1-X)^3+...(1-X)^(N-1))

Now the sequence in X is a simple geometric progression. If you let N tend to infinity, ie you are looking at the long term plateaued level of NO3 in your system the sum can be simplified and you end up with the following expression:

Final Plateaued Level= Y/X

So for example as mentioned by Tom in various threads if you do 50% WCs, or X=0.5 then your Max error is Y/(0.5)=2Y

i.e. twice the amount you dose between water changes.

Similarly 60% waterchanges give X=0.6 and thus gives the max error of Y/0.6=1.667Y

I just thought it might be an easy reference for people to figure out the maximum error they can have while dosing using EI so that they can be reassured that even if Sh*t happens, they won't harm their fish.

Cheers