Because of the inherent Johnson noise of any resistance, phono cartridges have a noise floor. It’s useful to know what that is so that design targets for phono preamps can be set. The cartridge resistance is surrounded by several reactances (e.g., the cartridge series inductance, the preamp input shunt capacitance…), so the effective noise resistance varies with frequency- you can’t just plug the DCR into the Johnson equation and get the right answer. Also, the noise from the cartridge is modified by the RIAA network in the preamp. So if a cartridge has an inherent noise of (say) 2uV, it really doesn’t matter if the preamp has 0.5uV or 0.005uV of noise, it’s buried behind the cartridge noise. In order to calculate this accurately, the audio spectrum needs to be broken into slices, calculations done for each slice, then the noise voltages RMS-summed. This is a major pain to do by hand, but trivial for a spreadsheet.
Here’s a handy-dandy little spreadsheet riaa calculator which allows you to calculate the maximum signal to noise attainable for a phono cartridge. Input the DC resistance, the inductance, the load resistance and capacitance at the preamp end, and the nominal output voltage, and voila, you know what you’d get with a perfect, noiseless preamp. This calculator is based on the equations given in the 1980 National Semiconductor Audio/Radio Handbook, using Q equations to transform the various series impedances (e.g., the cartridge L and R) into parallel impedances.
User inputs are shaded blue. I have used the spectrum slicing suggested by National, but you can vary that. The nice thing is that with the noise broken out into discrete bands, you can see the relative contributions from each frequency segment.
This was written in Office 2010 (xslx format), but if you have an earlier version of Excel, you can get a free converter from Microsoft.
Update: at the suggestion of Hans P, I have added an RIAA-weighted S/N as well as an unweighted S/N.