Calculating room gain

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Is there a way (other than by measurement - esp. if you don't have the equipment) - to predict / calculate room gain for a subwoofer?

Vented vs. a closed box design (for the same driver) - can yield upto 18Hz different in F3! (ie. F3 for a closed box Shiva MkII 12" is about 38Hz - vs vented (although larger box) = 21Hz).

I want to use a closed design - because it is supposed to give a better transient response (I mainly listen to music - and would rather have speed than bass extension) - however I feel an F3 of 38Hz is still too high for pop / rock music.

I know room gain will occur - it would be nice to be able to determine this - to see what the in room F3 would be of both boxes.

diyAudio Moderator Emeritus
Joined 2001
The merits of closed box versus ported box for the type of subwoofer you are building were discussed and illustrated extensively in the following thread:

Just one thing to add. Tests were run and it was discovered that the lower the bass, the harder it is for the listener to detect such things as distortion and phase difference. And 18 Hz is deep bass indeed.
the short answer is-measure it if you really want to know. The problem is that room gain isn't really a uniformly rising function.
Art Ludwig's site is pretty informative.

you can take a wild and semi educated guess at where the first room mode is by 565/L where L is the longest dimension of your room. if the longest dimension of your room is 20ft, then the first axial mode will be around 565/20=28hz. there will be a peak here, or close. how big will this peak be? well, how much polyfill is in your overstuffed couch?

Art Ludwig's site

as far as that whole sealed vs. ported issue goes, well, there are objective differences. sub-jectively(couldn't help that), the differences are subtle. best to listen to a well built sealed and ported version of the driver you're going to use and make up your own mind.

there are extraordinary TL, IB, sealed, ported, and others.

I know room gain will occur - it would be nice to be able to determine this - to see what the in room F3 would be of both boxes.

It's not entirely a fair comparison to simply look at the f3, as different designs have varying amounts of acoustic energy below f3. all things being equal, i'd take a TL at the same f3 than any other design, given it's shallow roll-off. (and if someone knows of a TL design with an f3 of 15hz, well, please let me know!)
ucla88 and kelticwizard - Thanks for the advice

I'll look through those URLs.

kelticwizard - one further question - you mentioned in the ported vs. sealed post that you should subtract the vent area (port * vent length) from the total internal volume. Is this with all programs?

diyAudio Moderator Emeritus
Joined 2001

Not sure about other programs. I mostly use Boxplot and AVI, which is DOS based and really simple.

If your program calculates the vent dimensions, try going from a 2" port to a 8" port diameter, (or as large as the program allows). If that doesn't change the plot, then the program is not taking the port volume into account, and you should do so.

Actually, vent volume is virtually negligible in many speakers, but in subwoofers going really deep it becomes significant and should be accounted for.

For Boxplot, I subtract the vent volume plus 10 percent, it just seems to work best that way. One way to check your program is this: fill in a speaker with these parameters:

Qts = .38, (or Qes = .41, Qms = 7)
Vas = 2 cubic feet
Fs = 30 Hz

Then run it in a 2 cubic foot box (Vas). Make Fb, the tuning frequency, equal to 30 Hz, (Fs). If the F3 isn't equal to the Fs, in this case 30 Hz., then calculate your correction factor. In real life, that is usually how it works out.

Incidentally, this is known as the "classic" bass reflex. That is, put a speaker with a Qts = .38, (or .4), into a box equal to it's Vas, tune it to Fs, and the f3 should equal Fs. Other bass reflex setups are possible, of course. Some designers find them even more desirable than the "classic".
kelticwizard... thanks once again... but just to clarify

I'm using the ported.xls spreadsheet from - simple but easy to use...

I entered your sample driver / enclosure - and got F3 = Fb = 30Hz - however when I bumped up the port diameter (therefore increasing the vent length) - the frequency response plot did *not* change....

does this mean I still need to subtract the vent volume from the predicted Vb? and in subtracting - does that mean I need to build the box smaller than calculated by the spreadsheet? - I would have thought since it does not take into account the vent volume - you need to *add* the vent volume to the enclosure volume.

eg. If you are meant to subtract.....
say the Vb = 57 litres (approx 2 ft3)- should I then make the Vb in construction = 57 - vent volume * 0.9 (being the additional 10% subtraction you state).

diyAudio Moderator Emeritus
Joined 2001

I should have made myself clearer with this "add/subtract" thing.

The vent is not to be considered part of the enclosure volume. You can either build the box larger to compensate for the vent, or lessen the box volume in your calcualtions.

Therefore, in construction, the box should be Vb PLUS volume of vent.

Under many circumstances the vent volume is negligible. In our above example, a 4" diameter port would be only 6% of the box volume. I wouldn't even bother.

However, if we make the port 8" diameter, our port volume is greater than the box volume. Even a 6" diameter port will use almost half the volume of the enclosure. If your plot does not change from a 4" diameter port to an 8", then clearly your program is not taking this into account.

If your program is showing an F3 of 30 Hz in our test box, then you probably don't have to allow an extra 10% assuming:

A) your vent volume is negligible-4" diameter is very generous for any speaker likely to go into our box, (3" diameter is more usual);

B) you are not putting an extraordinarlily large speaker in there-the speaker itself has a certain amount of volume as well. That has to be subtracted, but in most cases it is negligible.

I have built the test example and in most cases it comes out to an F3 of 30 Hz. So it works in most real-world instances. If you are going to use an extraordinary amount of bracing-well, then the bracing volume has to be compensated for.

Even if all these factors throw the calculation off by 10%, so what? You might end up with being 4 dB down at 30 Hz instead of 3 dB down? Not exactly something to keep anybody up nights worrying about, LOL.
diyAudio Moderator Emeritus
Joined 2001

We had a project discussed here where a Blueprint 1503 was contemplated being put into a 4 cu. ft box, tuned to 18 Hz. The Blueprint 1503 required either a 6" diameter vent with flares, or an 8" diameter vent without them.

The 6" diameter vent would take up about 21% of the box volume. The 8" diameter vent would take up about 70%.

As you can see, it is with subwoofers tuned really low that the vent dimensions really come into play. Subwoofers, and really compact speakers.

Incidentally, the fact that the vent cannot be counted as part of enclosure volume is the reason the Passive Radiator, (or "Drone Cone") was invented. It is a substitute for a vent. It takes some trouble and expense to make, so it is used in places where the size of the vent has gotten out of hand.
kelticwizard - ahhh.. I see - thanks.

I don't want to build the box larger than necessary.... (I'm quickly reaching Xmax on the SAF / WAF parameter - but I may as well test the limits.... :)

So I'll tune the box, then at build time add the extra space for the vent.

One last question (where have you heard that before? :)....

I read your reply to someones posting about "ideal" port diameter - you said you had lost the formula. David Weem's book suggests no less than 1/7th the area of your driver. Therefore for a 12" driver - no less than 5" (not flared I presume) would suffice (I know about the length of the pipe increasing with diameter - so will check it fits lengthwise for the Fb selected - and if not I'll "elbow" it).....

Anyway - my question - have you found the formula? Should I base the port diameter on some function of driver Vd? I'm probably being a bit pedantic about things - but know what can result when one "near enough" judgement is based on another "near enough" judgement .....

diyAudio Moderator Emeritus
Joined 2001

I read Weems' book years ago-Designing, Building and Testing Loudspeakers. It is where I got most of my knowledge. I have since read two anthologies from the Journal of the Audio Engineering Society, but if I had not read Weems' first book first, I would not have understood the Journal articles. There are some I still don't understand.

As I recall, when Weems speaks of speaker diameter, he generally means the actual piston diameter, not the diameter of the outside frame. For larger sized speakers,(12", 10" and 8"), that is usually 1 1/2" less than the outside diameter. Therefore, a 12' speaker is really a 10.5" piston diameter, approximately.

One seventh of a 10.5" piston 12.3 sq. inches, or a 4" tube. Almost exact agreement with your diysubwoofer calculations.

Back when I used the formulas, I discovered that they gave a generous figure-more than adequate-for the vent size. When I checked Peerless' recommended box and vent dimensions for it's speakers, the recommended vent is significantly smaller than the formula demanded. And these are the manufacturer's recommendations.

Many speaker manufacturers give the actual piston area in their specs.

By the way, I generally use PVC pipe for my vents. It does not appear to be available in 5" diameter.
Portsize follows Airspeed

My first post to diyAdio. OK here it goes. The one thing that should decide what port size you should have is what airspeed you get in the port. The speed depends on driver size, specs, box size and the power. It could be that you could use a smaller port for a 12" than a 10" depending on the driver specs. I suggest you download the excellent program WinISD (freeware by Juha Hartikainen) from
Read the very good help file included in the program its almost a like a, OK very short, schoolbook.
If you dont want to download and install the program i could make a qoute from the help in an E-mail.
another good way to play around with portsize and airspeed (and a LOT of other things) is Unibox300.xls (which I like very much).
Unibox download:


PS: Spell and grammar to be exused
Thanks keltiwizard

Yeah- I took that into account (well actually guessed at the true cone diameter on the Shiva 12" - at 11").

Weems' book does say from the outside edge of the surround on one side, to the inside edge of the surround on the other - in other words "mid surround to mid surround"

I was thinking last night - I'd like to try the box in both vented and sealed modes. If the box is large enough - although F3 will be raised (only by about 2 - 3 Hz over the lowest possible for a sealed (without EQ) - and the box Q lowered to 0.5 - it should make for a nice system when I want music precision = sealed - vs. lower extended bass = ported.

What do you recommend for plugging your port? (would you ever want to?).. now someone reading that sentence out of context might be offended :)

I thought of some sort of cork jar top - but maybe that may just get spat out at higher SPL (a time to put the mother in law in front of it maybe? :)

diyAudio Moderator Emeritus
Joined 2001
Dave Bullet:

I am glad that you have decided to build a convertible box. Personally, I am an unabashed advocate of the ported box, but people with real knowledge on this forum and others have recommended the sealed system, so it must have something going for it. Anyway, by building the convertible box, you will know for sure. I hope that after you are done, you tell us the results. Please tell us if your subwoofer sounds best:
A) Sealed all the time
B) Ported all the time
C) Sealed for music and ported for soundtracks

Also, by selecting a sealed Qtc of .5, you have selected the only speaker/box combo where you can have a system that works well in either sealed or ported modes. A Qtc much higher and the ported box will "boom"; a Qtc much lower and the sealed system's response will "droop" too much to be useful.

I haven't had time to check my local building materials store for parts availablility. But the project in the following link seems to supply the answer. It has nothing to do with sound, but the parts it uses seems to be precisely what you need, (I assume you are going to use a 4" diameter vent). You might as well buy the parts for both projects at once. Considering your last name, I have a hunch that once you finish the subwoofer, you will probably want to start on this new project-a potato cannon! ;)

Potato bazooka - the ultimate hero of SPL - maybe it could be made "beat activated" for that extra "hair standing on the back of your neck" when explosions hit the screen.

BTW did you know a blue whale reaches about 165dB when it calls - amazing huh! - I don't know who measured that - but that Radio Shack SPL meter is one hell of a versatile device :)

I will let you know how the sub sounds - construction is some way off however. Waiting for next pay packet, WAF approval at final design plans - must order driver and plate amp.

I'm going to cheat and get the timber yard to cut the MDF to size - I don't have a table saw - so will let someone who knows what they are doing.....

As for objective testing - all I'll have to go on is my own ears - unless I get an SPL meter and test CD.

I'm happy with the theoretical modelling of the box. My biggest concern was always with room gain - off to try winISD to see how it helps "guestimate" it.

As for vented boxes - there are many extremely good musical speakers out there based on the vented principle. Sadly, I think there is a lot of low end gear out there -vented seems to be a "cheap" way of getting extension - but because the tuning is bad or components used cheap those cheap systems have given vented boxes an underserved bad reputation.

Well - with my carpentry skills - hopefully I wont be adding to that stereotype (and if it does sound better sealed - I'll blame myself)

Thanks for your advice,
A good formula to calculate the minimum acceptable diameter of vent comes directly from R.Small, and according to him is 'strongly empiric':

Min_Diam_of_Vent = 0.56 * D(Speaker) *SQRT(Xmax)/SQRT(SQRT(Fb))
Measures in millimetres, Fb = tuning frequency in Hz

Now the lenght can be calculated with:

L = [c^2/(16*PI) * D^2/(Vb*Fb^2)]- (0.85*D)

Where :
D = the vent diameter previously defined
c = airspeed (normally 344 m/s)
PI = 3.1416...
Fb = tuning frequency in Hz
Vb = box volume in litres

In case the duct is too long/big, a good trick is to shape it in variable diameter, typically in sandglass shape (2 cone frustums joined by a constant diam.cylinder).
A software to calculate this vent is here, for those who can check an italian dictionary (click on ACS icon). page.htm

About the room gain question, it is very difficult to answer.
There are so many variables, like speaker emission (closed, vented, bandpass etc.), relative position to walls and floor, room dimensions and reflection rate etc.
I think it is impossible to make a 'reasonable' estimation with manual calculations, the sole CAD I know who can give some help is 'Audio for Windows', that is handicapped for being available only in Italian.
(the CAD is able to simulate speaker alignement, box dimensions, speaker position in the box, active or passive filters, room parameters etc. in the same project)

diyAudio Moderator Emeritus
Joined 2001

Your quote: "As for objective testing - all I'll have to go on is my own ears - unless I get an SPL meter and test CD."

That Radio Shack analog SPL meters is about $35. They go on sale a lot.

Test CD? Not necessary. Here is a nice tone generator that you can download free from the internet:

Click on "sine wave" for speaker testing. You don't have to go by the preset frequencies-just highlight the frequency display box in blue, and write in your own frequency.

Of course, there is nothing preventing you from using this tone generator to make your own test tape or CD, if you have a CD-RW.

For some reason, I cannot get this free program working right. However, other people on this forum absolutely RAVE about it. Perhaps I should re-download and try again. Anyway, it is a full scale speaker testing program and I am under the impression that you all you need is any decent sound card and a microphone to plug into it:

Good luck!
I agree in that I cannot see why you need an SPL meter - other than to know the actual SPL at a given frequency.

For example - use WinISD - to cut a CD playing a tone scale from 20Hz to 1Khz for example.

Play this on your regular audio amplifier (the one you will use to feed the high level inputs on the sub plate amp - coz' thats all I have) - then use a normal mic on the PC sound card.

Surely the normal mic - with appropriate software can tell you which frequencies are louder than others - after all its the relativity of frequency SPL that is important (who cares whether you calibrate the results to 80, 90 or even 100db - even though it might actually be 82.5 @ 100Hz etc...)

You can still get a good idea on F3, peaks and troughs, room resonance etc...

After all - all you need to know is how long your made up test track runs for, whether it progresses through the frequencies in a linear (or logarithmic etc...) fashion - then plot the inputs on a similar graph (ie. say you sample at 10 times a second - and you go up 10 Hz a second - therefore each measurement is 1Hz apart).

Of course a crappy mic, inaccurate sound card, where you measure (on axis / near field etc...) will affect it - but this will be consistent throughout a single run. You should then repeat with different positions / sub placements until you get either a consistent picture the alignment isn't right - or you position in the room with appropriate room treatments to get it right.

All too easy :)

diyAudio Moderator Emeritus
Joined 2001

I agree that a tone source of some sort and a microphone with calibrated output is all you need.

Now that I know that you have a CD-RW, I would just suggest that you break the sound spectrum into different tracks.

I've been thinking of making a test CD for friends, etc. I have an analog tone generator.

For instance, Track 1 would have a sequence of 4 seconds of 20,000 Hz, 4 seconds of 19,000 Hz etc down to 15,000 Hz.

Track 2 would have a sequence of 5 separate tones from 14,000 down to 10, 000 etc.

Of course, the lower you go, the closer you have to make the spacing between tones. Obviously, you don't want to go from 1,000 Hz to 0 Hz.

One advantage of doing it this way is that you always know which tone is being played. But of course, it is up to you-maybe you can think of a better way.
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