The best free tool I know of is the [u]SoX[/u] stats command. But, SoX is a command line tool so it’s not quite as easy to use as Audacity.
You might try Steve’s [u]ReplayGain[/u] plug-in. It can be used to find the relative loudness of a file (not the same as RMS). The ReplayGain analysis gives you the recommended change, so a louder file will give you a negative recommended dB change, and a quiet file will give you a positive recommended dB change, etc.
Adobe Audition has a similar feature, but it’s not free and it’s now a cloud subscription program. GoldWave ($60 USD) can be “tricked” into giving the RMS volume by running the Volume Match tool, which IMO is easier than Audacity’s Contrast analysis.