What does RMS mean in audio?

RMS stands for “root mean square.” It is a way to measure the average loudness or volume of an audio signal over time. Loudness is how strong a sound is. RMS tells you the typical loudness of a sound but not how loud the peaks (highest points) are.

RMS is often used with audio signals and electrical circuits that carry sound. It helps audio engineers set the right volume levels when recording music or making sound effects. RMS is also important for designing speakers, headphones, and other audio gear. Knowing the RMS power lets companies build their products to handle common volume levels without breaking.

RMS vs. peak level

To understand RMS, you must know how it differs from the “peak level.” The peak is the very loudest point in an audio signal. It’s the moment when the sound waves reach their highest point from top to bottom.

RMS and peak both measure loudness, but in different ways:

The peak level measures the single highest point
RMS measures the average level over the whole time

Imagine a simple sound like a quick drum beat. The peak would be the sharp attack of the drumstick hitting the skin. This part is very loud but only lasts for a flash. The RMS would be lower because most of the sound (the long decay after the hit) is quieter.

Now, think about something like a deep organ note. The volume stays steady for a long time. The RMS will be close to the peak level for a sound like this. There’s not as big of a difference between the average and the maximum.

Why is RMS used to measure audio levels?

RMS is super useful for audio because it matches how our ears hear sound. We don’t notice super quick peaks as much as the overall loudness over time. Two sounds with the same peak level can have very different RMS levels. The one with the higher RMS will sound louder to us.

RMS also works well when setting audio gear levels. Live sound systems and recording devices have to deal with constantly changing signals. The peak level might jump a lot, but the RMS stays steady for each sound source, making it a reliable reference point.

RMS and perceived loudness

Our brains pay attention to the average level of a sound over a few seconds. This is called the “perceived loudness.” It’s closer to RMS than the peak level.

You can have a sound with high peaks but a low average. For example, a snare drum has a big attack, but the volume drops fast. The RMS level is much lower than the peak. To our ears, the average level matters more than those short bursts.

Imagine you’re at a rock concert. The kick drum and bass make a steady, powerful sound. They have a high RMS level compared to the peak. Your ears will probably say the kick and bass are the loudest part of the music. Even if the snare drum or hi-hat have higher peaks, they sound quieter overall.

So, when audio engineers mix music or set up PA systems, they think much about RMS levels. They want you to hear the balance between instruments like you would naturally. An RMS meter helps them keep the average volumes in the right spots.

How do you measure RMS?

Measuring RMS in audio requires some math. You can’t just look at the waveform and find the RMS like you can with the peak. You have to calculate it using a formula.

The RMS formula does this:

Take a chunk of the audio signal (a short slice of time)
Measure the voltage or power at many points in that chunk
Square each measurement (multiply it by itself)
Find the average (mean) of all the squared values
Take the square root of that average

This gives you the RMS voltage or power for that chunk of audio. You can calculate it for the whole signal or measure it moment-by-moment. Most RMS meters take a new reading many times per second to track the changing levels.

The RMS formula

Here’s what the math looks like in an equation:

RMS = √((x₁² + x₂² + … + xn²) / n)

The x values are the voltage measurements at different times
n is the number of measurements you take
The √ symbol means to take the square root at the end

It looks complicated, but it’s not too bad. Let’s say you had a simple sound wave with these voltages:

2, -1, 3, -4

To get the RMS, you square each number, add them up, divide by the total count, and take the square root:

(2² + (-1)² + 3² + (-4)²) / 4 = (4 + 1 + 9 + 16) / 4 = 30 / 4 = 7.5

√7.5 ≈ 2.74

The RMS voltage would be around 2.74. That’s lower than the peak (4), but it gives a sense of the overall loudness. You can also square the RMS value to get the signal’s average power.

What units are used for RMS?

RMS can be expressed with different units depending on what you’re measuring. Audio voltage signals are usually in volts (V) or millivolts (mV). It’s typically in watts (W) or milliwatts (mW) for power measurements.

You’ll also see RMS levels given in decibels (dB). Decibels are a way to compare the loudness of different sounds using a logarithmic scale. The dB scale makes it easy to talk about big audio-level differences.

There are a few common decibel units you’ll see with RMS:

dBV: decibels relative to 1 volt RMS
DBU: decibels relative to 0.775 volts RMS
dBFS: decibels relative to the maximum possible digital level (0 dBFS)

So, if you have a signal with an RMS voltage of 1.55 V, that would be +3.8 dBV or +6 dBu. The formulas to convert between volts and decibels are:

dBV = 20 * log10(VRMS / 1 V) dBu = 20 * log10(VRMS / 0.775 V)

Audio gear often lists its maximum input and output levels in dBu or dBV. This tells you how big of a signal it can handle without distorting.

RMS power and wattage ratings

Regarding speakers and amplifiers, RMS power is given in watts. This is the average power a device can handle continuously without overheating or blowing out.

Imagine you have a speaker rated for 200 watts RMS. That means it’s designed to take an average power of 200 W over time. It can handle short bursts higher than that, but 200 W is safe for normal use.

You’ll also see “peak power” ratings on speakers and amps. This is the maximum watts it can take in a short burst. It’s always higher than the RMS power. For example, a speaker might be rated “200 W RMS / 400 W peak.”

The RMS rating is more useful for matching amps to speakers. If your amp can send out 100 W RMS, you want speakers handling at least that much RMS power. The peak ratings aren’t as important as long as the RMS levels line up.

Final Thoughts

RMS is a key concept in audio. It gives the average signal level in a way that matches human hearing. Measuring RMS voltages and powers helps engineers ensure that all the parts of an audio system work together.

Understanding RMS can help you set your gear properly as a music fan or musician. If you’re mixing a song, you can use RMS meters to balance the levels. If you’re buying speakers, you can pick an amp with the right RMS power.

RMS is a technical topic, but it mustn’t be scary. It’s just a way to assign numbers to the volume changes we hear in sound. The rest makes sense once you get the basic idea of averaging the squared signal.

Next time you see “RMS” on an audio meter or spec sheet, you’ll know what it’s telling you. It’s all about getting a steady look at a jumpy signal. RMS cuts through the peaks to reach the levels that matter.