audio - Getting loudness of a track with RMS

I'm trying to calculate the loudness of an audio track I have stored in a buffer. The buffer contains PCM data of the signal and I want to get how 'loud' it is by using Root Mean Squared. I assume I can do this in the time-domain instead of having to switch to the frequency domain. What would be the pseudo-code for doing this?

Would I simply sample for one second (audio[0] - audio[44099], audio[44099] - audio[88199] etc..) and calculate the RMS of those values? So, for example, would I do this:

$$RMS = \sqrt{\frac{\text{audio}[0]^2 + \text{audio}[1]^2 + \text{audio}[2]^2.....\text{audio}[44099]^2}{44100}}$$

for each second?

Answer

Another thing is that the RMS value is not very well correlated with perceived loudness. You might want to consider calling it level or volume instead. There is something called equal loudness contours which quantifies how sensitive the ear is to one particular frquency compared to another frequency, see the Wikipedia article. These curves are level dependent. For instance, the ear is very sensitive to a 1kHz tone compared to a 100Hz tone, as shown in this image (horizontal axis is frequency in Hz):

One of the relative simple things you can do is to filter your PCM data with an inverted equal loudness curve. Or you can apply the standard A weighting, see the Wikipedia Weighting Filter article. Then you can compute the RMS value of the output of the equal loudness weighted filter.