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Amplifier power / SPL calculator for home theater THX reference level

A question that frequently comes up when designing a home theater is ‘how powerful an amplifier do I need?’. The answer to the question depends on a few things, in particular how sensitive your speakers are and how far you sit away from them. When we design a home theater we want it to meet industry standards, in particular the THX standard for peak sound pressure level (SPL) at the listening position.

 

Remember THX Reference Level?

Reference level is a calibrated volume setting used for both movie production (in dubbing stages and post production houses) and reproduction (in screening rooms and theaters). Reference level for all channels except low frequency effects is calibrated by adjusting the audio chain such that a pink noise signal recorded at -20dB relative to full scale creates 85dB SPL as measured with a C weighted meter at the primary seating location. Peaks in movie soundtracks can therefore reach 105dB (0dB relative to full scale). For more read THX Reference Level Explained.

 

The 105dB peak SPL requirement

From the discussion of THX reference level the requirement is clear: amplifiers must be capable of cleanly driving speakers to 105dB SPL peaks at the listening location. Clean means that the amplifier is not clipping and total harmonic distortion (THD) is low – 0.1 or 0.2%.

 

Calculating SPL from sensitivity, distance and power

The SPL achievable at the listening location can be calculated if the following variables are known:

  • Speaker sensitivity – the sound pressure level (SPL) measured at 1m (3.3ft) from the speaker for 1W of input power*.
  • Listening distance – the distance between the speaker and the listener.
  • Amplifier power as measured in Watts (W).

*Beware that some speaker manufacturers quote sensitivity as 2.83V/1m. A speaker with 4 ohm nominal impedance uses 2W at 2.83V compared to 1W for a 8 ohm speaker.

Most of the online amplifier power calculators work in the same way. You enter the speaker sensitivity, listening distance and amplifier power and get SPL. We, however, are most interested in the amplifier power required to hit a certain SPL and so it makes sense to structure the calculation slightly differently.

Many people also make a simple mistake which effectively doubles the size of amplifier required. Using the online calculators they enter follow a process of trial and error to determine the amplifier size required for 105dB SPL. The issue is that our THX requirement is not for 105dB continuous output but 105dB peak output. More on this later.

 

Calculating the amplifier power required for 105dB peaks at the listening position

Our calculator works differently – we enter the sensitivity and listening distance to get the required amplifier power. SPL required is already known – we want 105dB peaks at the listening position to meet specifications. The calculator is shown below and can be downloaded Max SPL Calculator v6.

Max SPL spreadsheet

The main two line items in the calculator are Speaker Efficiency and Distance, which we have already defined above. From THX specifications the Average Program can be generically defined as 85dB and the headroom required as 20dB. The calculator then returns the Amplifier Gain required in dB and the Peak Amplifier Watts. You’ll see a number of options in the calculator to deal with various scenarios such as baffle wall mounting and sensitivity specifications that are not 1W / 1M.

Finally we see the Equivalent RMS Watts which is roughly half the Peak Amplifier Watts. The reason for this conversion is that all amplifiers spec sheets list RMS Watts, as measured with a sine wave. A sine wave has a 3dB crest factor i.e. the difference between average and peak is 3dB. So we effectively derate the calculated Peak Amplifier Watts by 3dB to get the equivalent RMS specification. This is an important point, and nearly everyone we hear discussing this topic online fails to derate the amplifier power requirements. They make the mistake of equating peak SPL with RMS Watts. In the above example an amplifier with a specified RMS output of 683W would actually give us 108dB peaks at the listening position, which is 3dB more than we need.  People using this approach will choose an amplifier roughly twice as powerful as they need.

 

Down the rabbit hole…

The approach to calculating amplifier power requirements for THX reference level reproduction presented above is of course a simplification. It will likely still give equivalent RMS amplifier power figures that are higher than needed.

The main reason is that an amplifier’s power output is higher for typical movie and music content than it is for sine waves. This Dynamic Headroom varies from amplifier to amplifier and can be as little as 1dB to as much as 8dB. Amplifiers with very robust power supplies tend to have low dynamic headroom and those with weaker power supplies such as your typical AV receiver high dynamic headroom.

A second complication for multi-channel is that often more than one amplifier channels share the same power supply.  The power supplies in these amplifiers are generally not designed so that the single channel power output is the same as the power output with all channels driven. The question then becomes what amplifier power specification you should look at when choosing an amplifier…single channel, two channel, all channels driven? Audioholics have a good article on this topic.

Thirdly we have the fact that speakers are not resistive but reactive loads where the real impedance varies over the frequency range rather than being a fixed nominal 4 or 8 ohms. This can result in over-estimation of amplifier power.

Fourthly the SPL in most listening rooms or home theaters does not fall off at 6dB per doubling of distance as the calculator assumes. The 6dB assumes free space. Often we have less than that, maybe 3-4dB. The importance of this is debatable, however, as I believe our 105dB requirement related to impulsive peaks not sound that has a chance to build up and is overlaid with the same sound that is decaying.

From the brief discussion above it is obvious that things get a lot more complicated in the real world. If you have any questions or corrections relating to this article please leave a comment below!

20 thoughts on “Amplifier power / SPL calculator for home theater THX reference level”

  1. Clear and valueable information on the subject. In some way we think the path to perfection was establish with all THX parameters, but in audio performance the auditioning will set the verdict, my opinion.
    For novices like me this rule of thumbs ended showing a way to a desired result. Why we don’t see such approach in HiFi, meaning two channels.

    1. Hi Tex,

      We can all use the same approach outlined here to calculate amplifier power requirements for two channel or stereo systems. The difference is that there is NO standard for how loud you should listen to music, unlike for theater where we have the concept of reference level which should be used by all post production houses when they mix down the movie soundtrack. For music I have seen written that during mixing engineers will use anywhere from 70-90dB SPL! Due to the Fletcher – Munson criteria really the recording will only sound balanced in terms of bass vs mids / highs when you are listening back at the same volume that the engineer used when mixing. If you listen to it quieter than the engineer then often times it will seem like there is not enough bass. Hence why tone controls are sometimes valuable.

      Thanks

      Nyal

  2. I have 4 Optima 250 power amps rated at 125 per channel. I also have 4 B&W LCR 600 S3 speakers. I would like to bridge each amp to run 250 rms to each speaker. Can I or will I get away with that connection? I can bi-amp each speaker if that will help.

    Please give me your opinion Mr. Mellor. Thank you so very much for your help!
    All the best,
    The Auerbachs

    1. Bridging an amplifier increases the power output. Generally speaking it’s better to have too much power rather than too little, since an amplifier clipping can produce nasty transients which can damage speakers. There’s no harm in having an amplifier rated for say 1000W RMS and a speaker that only has power handling of 100W RMS, as long as you are not over driving the loudspeaker by playing it beyond it’s capabilities.

  3. I have found your article the best I have seen on the subject. If you have the formulas used on the amplifier Power calculator, could be great to know them. Thank you so much for the article, it is fantastic.

  4. What a great summary of a straight-forward way to make sure you have enough power for your speakers. Thank you. I have a Denon AVR x3000 and am using Polk Audio RTiA3 speakers as mains. I wanted to use your tool to see if I was providing adequate power to them. The efficiency of the speakers is stated as 89 db and my listening distance is 12 ft. If I use your spreadsheet, I find I need to have an amp capable of 272 RMS Watts. Setting aside the fact the speakers are reccommended up to 150 Watts, my AVR only does 105 Watts per channel. However, if I lower the listening level to 81 dB, I find I only need 108 RMS Watts. Does that mean I should limit my listening level to <81 dB (still pretty high)? Just want to make sure I am using the tool correctly. Also, I am not running the mains as "Large", so shouldn't we get additional headroom if we cut them off at say 80 Hz? I didn't see that in the spreadsheet. Thanks for the help!

  5. Wouldn’t another benefit of a baffle wall be an additional 3 dB “boost” in speaker sensitivity due to the half-space arrangement? I’m thinking this would be another line item in the SPL calculations.

    1. Hi Bill

      Good catch! It’s actually 6dB gain from the baffle wall. Theoretically speaking this will increase the output of the speaker below the baffle step frequency (defined by the width of the speaker baffle – http://sound.westhost.com/bafflestep.htm). In practice whether this increases the max SPL output capabilities of the speaker depends on where the SPL limiting factor of the speaker falls. If it’s the woofer then yes it will increase output potential. If the tweeter is the limiting factor then no it won’t increase output potential.

      Thanks,

      Nyal

  6. I am also wondering if we could add lines in the amplifier power budget for speaker placement (baffle wall versus floor standing for example), use of bass management (which reduces stress on mains), and losses due to using an acoustically transparent screen (I think -2 dB is a number I commonly see). The use of EQ will also affect the numbers but that is hard to predict.

    1. Hi Bill

      Thanks for your comment.

      The output wattage of AVRs may be spec sheet 105W per channel but in reality it will be less than that with two or five channels driven. But is this important? There is some debate about this – see here for example: http://www.audioholics.com/audio-amplifier/the-all-channels-driven-amplifier-test-controversy.

      Where speakers do not specify power handling but rather specify recommended amplifier power they seem to often factor in amp headroom. So a speaker with a power handling of 75W they would recommend a 150W amp, to allow for 3dB of headroom. I know Martin Logan do this, but not sure about Polk.

      The spreadsheet is really designed for help specifying amplifiers when designing a system. If in reality when you have your system assembled you can play at reference level (85dB, with 20dB headroom) and you are not blowing up your speakers or your system sounds still as clear and crisp as at lower levels then I would not worry. There are many factors at work as I explain in the ‘into the rabbit hole’ section. The only real way to know would be to measure each system individually using some kind of test signal and monitor speaker distortion or other parameters. I do not know of any standardized tests for this.

      As I mentioned in my comment to your other question on the baffle wall post, whether to take the additional headroom into consideration depends on where the output limiting component in the speaker is (in the woofer, or in the tweeter), and how they specified speaker sensitivity (oftentimes this will be simply the SPL at 1kHz).

      Nyal

  7. Nyal-

    Thanks for the response. I agree that your spreadsheet is an excellent tool for spec’ing out an AVR/speaker combo. I just wanted to make sure I have accounted for everything that might matter.

    Once you’ve done all of your due diligence designing the system and you go ahead and make the purchases and set everything up, the proof is in the pudding and true system performance replaces the estimations. Hopefully you accounted for all of the major affects! One of things I am struggling with is how can I determine or get a feel for whether or not my current system can be played at reference levels (or close to reference levels) safely or without clipping and distortion. To me that is the only way to truely know how well your integrated system is performing. Problem, as you stated it, is there doesn’t seem to be a great way of doing that without just listening to it. I have been using REW a lot to look at frequency responses but I was hoping there was a way I could use it to help determine the maximum output of my system.

  8. Thanks so much for this calculator. It appears to encompass all of the factors that should be taken into consideration.

    I’m just using this for my HT setup in my family room. As such, there’s no baffle wall. When I remove the baffle wall from the spreadsheet (selecting No), RMS goes clear up to 637 watts, up from 160 watts before (89 db efficient speakers @ 4 ohms nominal resistance, with a listening distance of 13 feet).

    Is that accurate? I understand there are multiple factors that can’t be accounted for in a more open room than a theater setup, but that certainly drives up the required power for on-axis listening!

    1. Yes, the baffle wall gain is 6dB, that is 4x power! If your baffle wall is large enough it will support down to 80Hz. Most (but not all) speakers are SPL limited by the bass drivers.

  9. Is it possible for the genelec 8050b to hit reference level playback without compression at 3-4 meters from speakers? Thank you for you literature on reference level, great read.

    1. Thanks for your comment. That’s an interesting question, as the Genelec is an active powered speaker with DSP limiting built in. Here are some clues from the manual:

      1) Maximum short term sine wave acoustic output on axis in half space, averaged from 100Hz-3kHz @ 1m: 110dB
      2) Maximum peak acoustic output per pair above console top @ 1m with music material: 120dB

      The reference level requirement is 105dB peaks. That means 115dB at 1m for a 3m listening distance and 117dB at 1m for a 4m listening distance. Based on that I would say it would be very close. Note in 1) the output is specified into “half space” (in a test baffle which would have been shaped and cut around the baffle…kind of making the speaker an infinite baffle…that is how a lot of companies measure peak output) which provides a 6dB boost over “free space” (out into the room) mounting. If you put your Genelec 8050B in a baffle wall then you would get 110dB continuous and 113dB peak with sine waves.

  10. Nyal-

    I was poking around your site and noticed you updated your SPL calculator with some of the items we talked about last year. Thank you so much! One question. I noticed there is now a line for resistance. Am I correct in assuming this is the speaker impedance? If so, I was wondering why the defaul is set to 10 Ohms when most speakers are rated at 8 Ohms? Also, I was expecting that when I reduced the impedance, the required power would also go down but it’s the opposite. Maybe that’s just my ignorance on how impedance affects power ratings. Thanks!

    Bill

  11. I ran across your calculator while researching AV Receiver specs for a potential upgrade. It is very helpful, but I have some questions regarding how to apply this information to the current way in which manufacturers are stating receiver output specifications.

    As background, I am currently running a Denon 3808CI purchased in 2008. It has been a great receiver but obviously does not support the latest video or audio standards/technology. The Denon was purchased to drive an existing set of Klipsch surround speakers and its 130 watt per channel rating met the simple rule of thumb I had read somewhere at the time – make sure the receiver’s output rating was (at least) 50% higher than the max continuous rating of the speakers it is driving.

    I plan to drive the same speakers with a new receiver, and while meeting the THX requirement isn’t a “must”, it would be nice to have a set-up that could at least come close. When I run your calculator with my specific parameters the results are an RMS power requirement of 137 watts.

    Here are my questions:
    1. My front speakers are Klipsch SB-2s, rated at 85 watts maximum continuous input / 340 watts peak. I’m assuming that since the 137 watt calculator result equates to the peak sound pressure of 105 Db, the speakers can handle the 137 watt power draw if it only occurs only in short bursts – is that correct?
    2. It seems as though all manufacturers now state their AV receiver output specifications with “2 channels driven”, and I understand that the output across 5 or 7 channels will be some (indeterminate?) value less than this rating. Also, the cost of receivers that deliver 140+ watts across even 2 channels jumps pretty significantly from those that deliver say 95-110 watts. Some manufacturers now also provide a “dynamic” (or similar descriptor) power output at various impedances, which exceeds the “2 channels driven” output rating and is typically defined as short duration per channel power output that the receiver is capable of producing. Given this, is it reasonable to consider a receiver that has a “2 channels driven” rating in excess of the 85 watt speaker rating and a dynamic power rating in excess of the 137 watts generated by the calculator?

    Thanks, in advance.

    1. 1. Yes
      2. If the calculator shows a value of 137 RMS watts, then that’s the power rating your AVR would need to have to deliver THX reference level with the parameters you entered. Of course in the real world it may be less or more due to some of the multitude of complicating factors that I pointed out in the article. Depending on how aggressive or conservative you are in terms of your design process, you might consider ~140W at 2 channels driven enough, or you may want ~140W with all channels driven. Personally I normally take the 2 channels driven and de-rate it a little, maybe 10%, since it’s very rare for all speakers to be “on” at the same time

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