Measure RMS: stereo value - is it correct?

Sometimes I use the tools Measure RMS (rms.ny). I want to ask you - is that correct, that stereo value almost matches mono value? Should not be stereo value +3dB? I am comparing measurement results with iZotope Insight. (Of course it measures in LUFS, not RMS. This is just for demonstration.) Here is an example:

Measuring with Insight:

Measure RMS (rms.ny):
Similar result you can see here on the screenshot:

Of course, I can adjust the code of plugin: (_ “Stereo”) (+ (linear-to-db (stereo-rms rms)) 3.0) (_ “dB”))
…but at first I would like to confirm with you if I am not missing something. Thank you.

There are different ways to measure the RMS for stereo tracks. The way that rms.ny and Audacity’s “Contrast” tool do it (which is the correct way in my opinion) is to calculate the square root of the average (both channels) of squared sample values. This is (literally) the “square root of the mean squares” (which is what “RMS” means).

Sqrt ( (Left mean square + Right mean square) / 2)

An alternative way is the average of the two RMS values. This is easy to calculate, but it isn’t actually “RMS”. It is actually an “average RMS”.

(Left RMS + Right RMS) / 2

and a third way is the RMS of the average of left and right channels. This is actually the RMS of the channel average. Although this method is the easiest to calculate, it falls down badly because it gives wildly different results dependent on the relative phase of left and right channels. It should not be used for estimating loudness.

RMS( (Left + Right) / 2)

One (valid) way of thinking about this, is to imagine that you play a mono track through a pair of stereo speakers, and then measure the loudness.

Then duplicate the mono track and combine the two mono tracks into a single stereo track. When you play this stereo track through the same stereo speakers, the same sound is being sent to each speaker as in the first case, and it will sound identical to the mono track.

Thus if you have a mono track that measures as -23 dB RMS, and you combine it with an identical mono track to create a stereo track, then the stereo track will also be -23 dB RMS.

Thank you for your kind explanation. I appreciate it a lot!