# How big amplifier do I need in terms of Watts?

## Tutorial with power calculator to determine how many watts the amp must be

How many watts do I need? How big should my amplifier be? How much amplifier power do I need? These questions are asked over and over by many people and here’s a nifty little power calculator and some logical arguments may help you reach an answer.

Firstly, writing this guide without going over board by dabbling in the details only to end up with a huge document that nobody will bother to read demands that we make a lot of simplifications. However, these simplifications will not affect the core logic behind the arguments, and at the end of the day all this will be is an estimate to guide your decisions of what constitutes enough power for your application, and for that purpose these simplifications will not misguide you, but rather make you less confused.

That being said, I’m happy to discuss shortcomings of manufacturer’s stated specifications, room gain, anechoic chambers vs normal listening rooms etc in the comment section below.

## Amplifier power calculator

To help you figure out how much amplifier power you need I’ve created this helpful calculator. To understand how it works I strongly suggest you read the article to understand the logic behind it, but you can also view the video tutorial on how to use the power calculator if you just want to do a quick and dirty estimate.

If you don’t understand how to set crest factor and average listening level meaningfully, set crest factor to 0 and set the average listening level to the loudest you ever listen to music.

PS: If you would like to use the amplifier power calculator in the future, it’s also available on its own small page so you don’t need to load this whole article.

## Speakers and specifications

First, let us consider a pair of speakers where the manufacturer’s specification sheet states that they have a sensitivity of 85dB, an impedance of 8Ω and a power rating of 300W.

Will an amplifier rated at 300W at 8Ω suffice, do you need a bigger amp or can you get by with a smaller amp?

To answer this question we need to answer an array of questions, so let’s begin by takling about the speakers. They have a sensitivity of 85dB, and a sensitivity of 85dB means that if you feed the speakers 1W they will produce 85dB worth of Sound Pressure Level or dB SPL, at 1 meter (or approx. 3.3 feet).

You probably don’t sit 1 meter away from your speakers, and because Sound Pressure Level drops by 6dB for each doubling of distance, the sound will be lower in volume where you actually sit.

So again, if a loudspeaker is 85dB efficient at 1 meter, it will be 79dB at 2 meter and only 75.5dB at a 3 m (10 ft) distance when the input power is 1W.

So let’s assume you are 3 m away from the speakers, and you get 75.5dB SPL when your speakers are feed 1W of power. That may sound like a lot considering that a person speaking to you from about 1 m away with a normal voice is about 60dB SPL.

At the same time 75.5dB is not really all that loud, many audiophiles and music lovers like to listen at an average level of about 80dB. Notice that I wrote «an average level of around 80dB», this is important, because the average doesn’t tell us all that much because music have dynamics and this is where we arrive at something called the crest factor.

## Crest factor explained

Simply put and in relation to music, crest factor can be defined as the difference between the average level and the maximum peak level.

In a dynamic piece of music the hit of a drum will be much louder than the average level, so the hit of the drum will increase the crest factor. Say the average level is 80dB and the sound of the drum hitting is 100dB, that’s a crest factor of 20dB. Music typically has a crest factor between 10 to 20 dB, but sometimes even more than that.

Music with a high crest factor is insanely dynamic. It sounds spectacular and grandiose, while music with a low crest factor more often than not will sound aggressive and give you early listening fatigue. Furthermore, music with a low crest factor is typically a victim of the infamous loudness war. Everything is loud; the vocals, the instruments – everything. The average level is high all the time, there’s no dynamics.

When you are playing music with a low crest factor, you will normally turn down the volume, because the lack of dynamics make the whole song sound loud.

In contrast, dynamic music will make you increase the volume, because it isn’t fatiguing even when it hits that loud drum that makes you shut your eyes on a reflex.

The point of this being that if you enjoy music with lots of dynamics you need to have enough amplifier headroom to reproduce those dynamic peaks of up to and above 20dB.

## Amplifier power in relation to sound pressure level

You may have heard this before, but it can’t be said enough times. For each doubling of power you get a 3dB increase in sound pressure level.

Think about that for a minute. When you double the distance from your speakers you lose 6dB of SPL. That means you need four times as much power to get back to the same level, because you only gain 3dB for each doubling of power(!)

This is why you should sell your stereo equipment and buy a pair headphones with a high quality class A amplifier with 5W of clean power, haha. But seriously though, it’s quite crazy to think about this relationship and how amplifier power and distance relates to one other.

Many manufacturers are measuring their amplifiers by hooking up a dummy load and cranked up until it reaches 1 % THD+N (Total Harmonic Distortion plus Noise). So when the spec sheet says an amplifier gives 30W into 8Ω it means that when an 8Ω speaker draws 30W from the amp, the amp will deliver that power with a signal distorted by 1 %.

When the amp is delivering 1/2 the rated power distortion will be lower, and when it delivers 1/4th the power even lower, and 1/8th the power lower still. Do you notice a pattern here?

If you look at the graph above you see that the distortion is starting to rise at about 10W and then shoot up at around 25W. Furthermore, notice that there is more distortion below 0.5W than from 0.5-15W.  Interestingly, many amps have more distortion when they are hardly used than when they’re being pushed a bit.

You may also wonder what those three different lines are. Each one is for one frequency. So you can see that an amplifier will distort more for some frequency and less for other frequencies. This amp measures very well and is almost linear, other amps distort unevenly, so you have more distortion in the bass than the mids for example.

So now you’ve probably caught on to the benefits of amplifier headroom. You don’t want to push your amplifier to its limits. Very few things like to be pushed to the limits. If you give the amp breathing room and as optimal conditions as possible it will last longer, it will produce less distortion and you will enjoy it more. It’s really just common sense and good practice.

Personally, I like to have 9dB of amplifier headroom, but there is nothing wrong with 3-6 dB either. In terms of power 3dB headroom means you’re using 1/2 the rated power, 6dB means 1/4th and 9dB means 1/8 and so on. So on an 80w amp you would ideally just use 10W if you want 9dB of headroom – now that’s sick!

Of course you don’t have to follow such rules and I admit that 9dB of headroom is quite a lot, but 3-6dB is very good practice.

## Recap of what we know

1. The first watt will give you a lot of loudness, how much depends on the sensitivity of your speakers.
2. For every 3dB extra you want after that you need to double the amplifier power
3. For each doubling of distance from the speakers you lose 6dB
4. Our amplifier needs to be able to reproduce music with a high crest factor, sometimes above 20dB
5. You want 3-9dB of amplifier headroom

So planning for the extreme and assuming your speakers can even handle it, lets’ look back at our example.

You are still 3 m away from the speakers, and you get 75.5dB SPL when your speakers are feed 1W of power.

You want to have an average level of 80dB, an additional 20dB to reproduce the dynamics (crest factor) and you want the amp to have 6dB of headroom so it’s working under very optimal conditions yielding very low distortion and full control of your driver cones. How big must the amp be?

Well, we need [(80+20+6) – 75.5] = 30.5dB of amplification, and because each doubling of power only gives us 3dB we need to double our power 30.5/3 = 10.2 times(!), that means we need 2^(10.2)  ≈ 1150W of power!

But wait, the speakers were only rated for 300W, the voice coils will fry and the cones will shoot across the room!

No, remember we have 6dB of amplifier headroom in this case, so we won’t feed the speakers 1150W, we will only feed them 1/4th of that, so 1150/4 = 288W and that’s within the power limit of the speakers.

A 300W amp would be able to deliver the same SPL as the one with 1150W or more, but we would hardly have any amplifier headroom left, the amp would be close to maximum capacity and the performance wouldn’t be as good as with the bigger amp.

In addition, and very counter intuitive is that fact that it’s not a too big of an amp that blows speakers, more often than not, it’s an underpowered speaker that blows as the amp becomes unstable and distorts like crazy while clipping and the smell of burned glue and rubbing voice coil windings become reality, hence a big amp is also beneficial in protecting the speakers(!)

## Conclusion & discussion on amplifier power

From this example we’ve learned a few important lessons, one being that an amplifier bigger than the power ratings of the speakers will yield better performance and be safer for your speakers.

A simple rule you can use is to look at the power rating for your speakers, and if you want 3dB of amplifier headroom you want double what the rating says, if you want 6dB of headroom you want four times as much power and if you want 9dB headroom you want eight times the speakers’ rated power.

That may seem like a lot of wasted power, but you can’t think of it that way. It’s like saying your car could do 230km/h, and because you drive 100km/h now and then, you are wasting 130km/h. Do you think your car would be happy to be driven at 230km/h just because it can? Nope. The same goes for audio amplifiers.

That being said a lot of people will be happy to under power their speakers, but if you want good dynamics and keep those cones in check you want the power. It’s as simple as that.

### How to get by with a smaller amplifier

Instead of getting a big amplifier you could go with a highly sensitive system. The problem is that an efficient system will be very large, especially if you want to cover the full audio spectrum and reach 20 Hz (or even below that) with any kind of real authority.

You already know that doubling the amplifier power will yield 3dB of output, but did you know that doubling the surface area will theoretically give you 6dB of extra output (if they combine acoustically)? Well, that’s only theoretical and if you double the surface area you are also going to double the power as you’ve got two subs and they both require power. So you actually get 3dB for every doubling of surface area and 3dB because you are also doubling the power. At the same time you may have an 8 Ohm sub, if you wire two subs for 4 Ohms and connect them to an amp able to drive this load you will get “free power”. Depending on the amp and how hard you drive it, you will get some additional distortion running it in 4 Ohms compared to 8 Ohms, but it’s likely to be negligible.

The reasoning above basically this means that if you have one 18″ subwoofer, getting another one and placing them within 1/4th the wavelength of the highest frequency they produce will be better than doubling the power to one sub, mainly for two reasons. (1) More surface area means less excursion (driver moving backwards and forwards) which in turns yields less distortion. (2) You may get “free power” if you wire the subs up to a lower load your amp can supply.

To get an additional 6dB, you need four subs and then eight for another 6dB, then sixteen and so on. This is all theoretical, sometimes you get a lot more at certain frequencies and sometimes you get less. You may even get cancellations. Also notice how the system will grow exponentially in size and cost if you want that extra output. To find the best balance between surface area and power you need to consider what the cost of doubling the surface area will be in terms of money and the capacity of your electrical wiring against the space and cost added by doubling the subs.

So unfortunately, there just is no free lunch, and truth is that a bigger system with a smaller amp will always be better than a small system with a bigger amp.

Just think about the forces and the dynamics in a thunder storm. It’s quite optimistic to expect that a few vibrating cones and a small tweeter is able to reproduce that kind of dynamics no matter what power you put behind it. The big system can’t even do it, but it will do it better than the small one.

We also discussed amplifier power and how headroom benefits you in the form of lower distortion, but the biggest and baddest source of distortion are the speaker cones themselves. The louder and lower they play the further they will move. You can quickly run out of excursion in the lowest octaves but long before you rach xmax you have a big percentage of distortion. This is because the voice coil is outside the motor’s linear magnetic field, and the only thing you can really do to avoid this is to get more or bigger drivers. This is one of the major benefits of big subwoofer systems. All subwoofers work less which in turn yields less distortion and more realistic and dynamic bass.

Oh, and by the way. The reason why the subs must be within 1/4th the wavelength of the highest frequency is because that will make them acoustically coupled. Here’s a small calculator to find the wavelength of a frequency and fractions of that wavelength.

### Compromising on bass yields higher sensitivity and better dynamics

Another thing people do to keep their systems’ WAF high and the amp smaller while still preserving some dynamic capabilities is to skimp on bass. They compromise on bass reproduction, because bass is where most of the power is burned and bass introduce room modes and acoustical problems that has to be solved with DSP and/or physical acoustic remedies, which they just can’t be bothered to address.

Using DSP to boost certain frequencies, particularly in the lows, will also cost a lot of amplifier power and eat up your headroom. On the other hand, if you have too much room gain and you use DSP to lower the level of low frequencies you give the amp less work.

When people forgo bass and reproduction of the lows is no longer a concern, the sensitivity of a speaker will increase, because the tweeter is very efficient. Reproduction of bass is what takes the most power and demands the bigger system. The cost of skimping on bass is loss of realism, as real world is full of sounds that contain bass.

So basically and in short; the ideal system is large with a very high sensitivity and the amplifiers have 3dB or more headroom relative to the maximum peak you will ever reach with the system under your most extreme use.

## Discussion on How big amplifier do I need in terms of Watts?

1. Matthew Dickinson says:

Thanks for this, but since it is "Headphone Addict" at first I thought it would be for headphones!

by the way (or not so by the way), I bought this cheap \$15 dac-amp off eBay, one of those DIY board things…

http://www.ebay.com/itm/301291337458?_trksid=p2057872.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

and it sounds about as good as the \$300 (originally) Beyerdynamic / Astell&Kern "A200P" (or Ak10, as it was originally called). I have that and was comparing with PX-100ii and T51i and DT 1350.

It's noisier, though: picks up noise from the computer through the USB cable. I probably should have bought the version with the case, but I'm not sure that would have helped with the USB noise.

I think it actually seems to have a bit more punchy and raw sound to it… am I crazy? I have trouble telling the difference between DACs and amps, at least in my limited experience. I will try things like an old Sony Discman, or PlayStation Vita, and some other sources, for comparison, but not hear a lot of difference.

I guess I have been reading too much of the NwAvGuy's writings and it's filled my head with too many evil thoughts about the audio industry and the basic similarity in sound between most amps and DACs… they're supposed to be transparent.

But it would have been nice to have bought one with a little less noise and a little more power…

I guess I might go shopping again

Matthew