Nitrate readings. ppm, mg/L, and meq/L?

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Whilst researching another persons troubles I realized or rather learned that the common test kits do not all test for the same molecule and there are sometimes conversion factors one should consider. I tried to find an old Randy article or R2R thread that discussed the topic in detail, but was unsuccessful in my search. Can a chemist here possibly illuminate the subject? What are the different molecules commonly used to test nitrate and how does one convert the readings or all all test kits already converted in their accompanying chart?

Thanks to one and all.
 
To start, for most purposes, parts per million (PPM) and mg/L are the same thing. On meq/L (milli equivalents per liter), I've only seen that used in our hobby to describe alkalinity.

Nitrate is either reported in PPM nitrate, or PPM NO3-N (which is nitrate as nitrogen). You can convert from one to the other. To convert from Nitrate-N to Nitrate, multiply by 4.4.

To my knowledge all our aquarium kits report in PPM Nitrate...So if your kit says 20 ppm Nitrate, then Nitrate-N would be about 4.5 PPM.
 

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