Normally you'd load it into an editor and find the peak then find the silence - subtract one from the other and you're done. No need for a plug-in - virtually every editor has these kinds of features built in, as do many of the DAWs. Other ways are to normalise the entire track to 0dB, then find the noise, and read off the direct figure as dB below 0. Or even take that noise sample and normalise it, if your DAW/editor gives a reading of the amplitude increase - if it has to increase is by 60dB to get to 0 - same end result.
The problem with automating it is that leaves you to make judgements on what is being measured. I've done this myself where the maximum level the DAW sees includes a little glitch somewhere that gives one of those one or two sample spikes that often you don't hear. I suppose technically, the range produced would be made to be greater than it really is, based on the real music content. I'm talking about those rare tracks that when you normalise them, the waveform still looks low, and if you track it down it's a very. very short transient. If you then reduce or remove that, normalisation then increases the whole thing in level. Trouble is sometimes that's then too late to cure the rise in the noise floor which is fixed. Can of worms. Opened.