I didn't grow up with S.I units but logic tells me that with metric dimensions it should be relatively easy to equate any pot linear measure to volume as there is a direct intrinsic link - a cubic metre of water for instance weighs 1 metric tonne - the only trouble with this thinking is that it might not quite coincide with compost folk's opinion.
Maybe @SporophyteBoy but if you have a standard unit with known parameters you have everything you need surely, NTP is used widely but never quoted. Many pots are described by volume but this doesn't tell you the shape so some mechanism for describing height and width would also be useful don't you think?
Something like R2/6 a round pot twice as high as wide and volume 6L or S1/1 and so on.
"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." Sir Terry Pratchett
Trouble is - I go back to clay pots that hadn't changed shape for about 2,000 years - some of the ones I had to clean in the first nursery I worked in still had Roman graphito!
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Something like R2/6 a round pot twice as high as wide and volume 6L or S1/1 and so on.