The RMSD of the electron density (or difference density) is calculated by the FFT program using the standard equation that I referenced. I would guess that what you see in Coot is copied either from the map header or the FFT log file.
I'm not clear what you mean when you refer to 'the
e/A^3'. The RMSD (as does the electron density from which it's calculated) consists of a pure number and a unit of measure, e.g. '1.234 A^-3' (why it's not '1.234 eA^-3'
we won't go into here: suffice it to say that 'e' is a unit of charge and 'electron density' is not the same as 'charge density', while an electron, or 'e-', is not a unit of measure at all, it's a sub-atomic particle: see Wikipedia/Non-SI_units_mentioned_in_the_SI and
Wikipedia/electron). The relation between 'RMSD' and 'A^-3' is simply that the latter is the unit of the former, exactly analogous to the relation between 'distance' and 'metre'.
Yes '3 sigma' in this context is not correct: it's '3 RMSD', and indeed COOT itself uses the latter terminology (which you see any time you change the contour level), so I'm not clear where you got that from. The uncertainty ('sigma') of the density does have a value, though this is not estimated by any of the standard programs AFAIK. However one thing is certain: it's unlikely to equal the RMSD!
