RMS Explained In Plain English (And A Little Algebra)

TL;DR – RMS helps us measure the average level of a source over a given (usually short) time period. These measurement tell our audio meters how weak or strong a signal is.

How does it work?

Let’s go back to your high school algebra class and define our terms. RMS is an acronym.

Root – square root

Mean – average of a set of numbers

Square – Giving the value an exponent of 2 (x²)

Putting it all together, we do the square root of the average of our given values after they’ve been squared.

Why do we need RMS? Can’t we just do the mean?

RMS accounts for both positive and negative values in and audio signal (since sound is a pressure wave that creates alternative positive and negative pressure). The “square” part of RMS makes every number in the calculation positive, so we can come up with a single value for the “average” level of our signal.

Exactly how many numbers do we have average to get good data? Does more averaging mean better data?

How quickly our output value tracks with the incoming signal is determined by our RMS Window. If our equation constantly recalculated to include each new number, but never reset, our RMS Window would be infinity. Our final calculation would include ALL of the data accrued over a certain amount of time.

Making our RMS window short (300ms) gives us a snapshot of the average level for that period of time.

Let’s see this in action.

Let’s set our RMS window at 4 “values” per second. Our equation looks at the incoming level evenly four times over the course of 1000ms, so every 250ms, we get a new number (let’s not worry about units for now). Much like frame rate on a camera.

Here’s our values:

5, -3, 2, -7

Now let’s square them:

5² = 25 -3² = 9 2² = 4 -7² = 49

Here’s the mean:

(25 + 9 + 4 + 49) / 4 = 21.75

The square root of that:

sqrt(21.75) = 4.66

Boom, 4.66 is our RMS value of the signal level over one second, using a window size of 250ms.

mkc