Study Hall
Audio Technica

# Watt’s That? Confusing Amplifier Ratings And SPL Specs

## Even though it's a common misunderstanding, loudness is not measured in watts.

By Jonah Altrove December 4, 2017

During a recent training, we were comparing powered loudspeakers and the question was asked, “This one’s louder, right? Because it’s got more watts?”

Hear that sound? It’s me sliding my soapbox into place. This comes up over and over, and it’s a common misunderstanding, so let’s straighten it out: Loudness is not measured in watts.

You could hardly be blamed for thinking so – powered loudspeaker ads prominently feature wattage readings, while the far more informative max SPL stat is usually buried in the multilingual chart on the last page of the manual, along with other fascinating parameters such as the fuse type. This speaks volumes (get it?) about what the manufacturers think that we think is important.

In my neck of the woods, people use time to measure distance – we say, “Oh, that town is about three hours away.” This works because there is an implicit understanding of the other variable – the speed limit.

When we talk about a higher-wattage loudspeaker being louder, we’re doing the same thing – describing loudness with a parameter that isn’t the correct one, but does factor into the equation. The problem in this case is that we’re making assumptions about the other factors, and this time, they’re poor assumptions.

## Various Variables

Why, then, do we do it? Because it works – sort of. A loudspeaker is a transducer, a device that converts one form of energy into another. So it’s certainly logical to expect that more (electrical) power at the input means more (acoustic) power at the output.

Unfortunately, since other variables are involved, all we can say is that the input power and output power are correlated. Correlations are tricky, because there’s often more going on.

Example: Children having larger shoe sizes tend to have better math skills. Why? Because older kids have learned more math and have bigger feet than younger kids. There’s a correlation between shoe sizes and math skills, but we shouldn’t quantify math skills in terms of shoe size. (Although I’d be okay if we did, because my feet are so big that my old footwear could be used as housing for displaced refugee families.)

So let’s understand the other factors. There are several, but the critical one is a loudspeaker’s sensitivity rating. Back when the world was flat, everything was black and white, and passive loudspeakers were the only option, we determined loudness based on sensitivity rating and maximum power handling. Sensitivity tells us how much output to expect for a given input. (And maximum power handling tells us when to expect smoke as an output.)

As Bob McCarthy says, our industry standard is to have multiple standards, but the most common way to measure loudspeaker sensitivity is to state the sound pressure level (SPL) that would be measured from 1 meter (m) away at a power level of 1 watt (w). A typical spec might be 97 dB SPL re: 1 w/l m. (This is often incorrectly shortened to simply 97 dB.)

Paradoxically, the sensitivity is often actually measured at 2 meters rather than 1, because the closer measurement may place the microphone in the loudspeaker’s nearfield, so it doesn’t behave like a point source and can mess up the measurement. So we can measure it at 2 meters and then add 6 dB. But that’s neither here nor there. (Get it?)

Once we know the sensitivity, we can calculate SPL for a given input power, up to the max power handling. With power, the formula is 10 log (ratio), so 2x power = 3 dB and 10x power = 10 dB. Raising the input power from 1 watt to 2 watts is a 3 dB increase over the 1 watt reference case, so 97 + 3 = 100 dB SPL. How about 10 watts in? That’s 97 + 10, or 107 dB SPL.

Let’s say the max power handling is 300 watts. We can use the formula to find max SPL: 10 log (300 w/1 w) = 25 dB, and our max SPL is 97 + 25 = 122 dB SPL.

A driver with a higher sensitivity (maybe 100 dB SPL re:1 w/1 m) would give more output for the same input, and now we can see why we can’t just look at amplifier power – we also need to know the loudspeaker’s sensitivity and power handling limits in order to talk about maximum SPL capabilities.

## Making Decisions

The twist is that powered loudspeakers take care of the math for us, since their drivers and amps are a closed ecosystem and we don’t need to worry about matching them up. Rather than calculate max SPL like we just did, we can just print it in the user manual. (The max SPL stat, however, suffers from its own complication – see “What’s The Response” by Charlie Hughes.

There are countless design and engineering decisions that guide a manufacturer’s selection of components, but at the end of the day, printing an ad showcasing a powered loudspeaker with a fire-breathing onboard amp is way more impressive than printing a driver sensitivity. Consider that we can net a +3 dB improvement by either going from 97 dB SPL re:1 w/1 m to 100 dB SPL re: 1 w/1 m sensitivity, or by going from a 1,000-watt amp to a 2,000-watt amp. Which one sounds cooler to you?

End result: We buy a new loudspeaker with a higher power rating and it’s louder. All things being equal, this is true. But we need to remember that wattage isn’t the only variable in play. A non-technical analogy: [All things being equal,] a more powerful engine makes a vehicle faster. But we cannot assume that a vehicle is faster than another because it has a more powerful engine.

And by the way, we can say the same about SPL, which is related to perceived loudness, but not a measure of it. (Ever heard of a “sone?”)

## Being Informed

I realize that I can’t single-handedly stop people from equating watts to loudness, and time for future musings would be better spent on other things, like thinking up a witty closing line.

But as I said regarding the difference between phase and polarity (Phase Vs Polarity: The Struggle To Understand Pro Audio’s Most Pervasive Inaccuracy from LSI June 2017), those of us who know better should try to get this right, because those who don’t know better will learn from us. It may not stick, but at the very least, we’ll all be better informed.

Remember: Knowledge is power… and loudness is not. (Get it?)