Useful Formulas
This section outlines some information you will need to manually design your enclosure if you are using a scientific calculator, or if you are interested in the formulas involved. You will need the Thiele/Small specifications for the driver you want to configure, and at least a rudimentary knowledge of math. Check out the Software section, which lists some free programs to download for designing your enclosure.Remember, all data when figuring speaker enclosures is theoretical! Designing enclosures is not an exact science, and sometimes what is perfect on paper or a software graph can be improved upon by listening and making adjustments to the system. Use your ears!
Metric to English |
Multiply Metric Unit by: |
| mm to inch (linear) |
0.03937 |
| cm to inch |
0.3937 |
| meter to foot |
3.2808 |
| square cm to square inches |
0.155 |
| square meters to square ft |
10.763 |
| cubic meters to cubic ft |
35.314 |
| liters to cubic ft |
0.0353 |
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English to Metric |
Multiply English Unit by: |
| inch to mm |
25.4 |
| inch to cm |
2.54 |
| foot to meter |
0.3048 |
| square inches to square cm |
6.4516 |
| square ft to square meters |
0.0929 |
| cubic ft to cubic meters |
0.02831 |
| cubic ft to liters |
28.32 |
Note: Unless otherwise specified, all formulas use English measurements.
^ = exponent, for example 10^3
Efficiency Bandwidth Product (EBP)
To help you design the correct enclosure for the driver you are using, first find the Efficiency Bandwidth Product of the driver:
EBP = Fs / Qes
50 or less = best used in a sealed enclosure.
50 - 90 = flexible enclosure options.
90 or greater = best used in ported enclosure.
For more information about EBP and designing sealed and ported enclosures, check out Enclosure Dilemma: Ported vs. Sealed.
Optimum volume for sealed enclosure (cubic ft ):
You may substitute any Qtc between 0.50 and 1.50 in place of 0.70 in both equations (both must have same value) to experiment with enclosure size. Qtc of 0.70 is generally considered an optimum alignment, with very good transient response, low cut-off frequency, and flattest response to the cut-off - See Qtc.
Note: You must always choose a Qtc higher than the driver's Qts!
Find alpha: X = (0.70 / Qts)^2 - 1
Then calculate enclosure volume: Vb = Vas / X
System resonant frequency: Fcb = 0.70 / Qts ( Fs)
To find the theoretical cut-off frequency, use the following chart to find the F3 factor:
Qtc |
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F3 Factor |
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Qtc |
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F3 Factor |
0.50 |
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= 1.55 |
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1.00 |
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= 0.79 |
0.60 |
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= 1.21 |
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1.10 |
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= 0.76 |
0.70 |
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= 1.0 |
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1.20 |
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= 0.74 |
0.80 |
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= 0.9 |
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1.30 |
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= 0.72 |
0.90 |
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= 0.83 |
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1.40 |
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= 0.71 |
Then: F3 = Fc x (F3 Factor)
Optimum volume for ported enclosure (cubic ft):
These formulas were engineered by D.B. Keele Jr. using the vented enclosure alignments developed by A.N. Thiele.
Enclosure volume: Vb = 15 Vas (Qts^2.87)
Theoretical cut-off frequency: F3 = 0.26 Fs (Qts^ -1.4)
Tuning frequency: Fb = 0.42 Fs (Qts^ -0.9)
If an ideal box is to large for your application, choose an enclosure size in cu.ft. then
Find: F3 = (Vas / Vb)^1/2 (Fs)(an exponent to 1/2 is the same as taking the square root)
New tuning frequency: Fb = (Vas / Vb)^0.32 (Fs)
Note: these formulas for the "ideal" enclosure provide a flat response curve, reasonably low F3, and fair transient response. The smaller you make the enclosure, the larger the peak in the response curve, the higher the F3, and the poorer the transient response. Enclosures much smaller than the "ideal" alignment will sound muddled and boomy.
Optimum volume for single reflex bandpass (cubic ft ):
Determine Vr with above formula for a sealed enclosure. The 4th order bandpass design is optimum with a total system Q of 0.70, using a Qtc and S of 0.70 for Vr (sealed portion) and Vf (ported portion).
Vf = [(2) (0.70) (Qts)]^2 |
Vas |
Vftuning frequency: Fb = (0.70) (Fs / Qts)
The system F3 for a properly designed bandpass will be lower than a similarly damped sealed enclosure. Depending on the System Q and tuning, F3 can be up to approximately 1/3 octave lower (or more) if system Q parameters are the same for both types of enclosures using identical drivers. Bandpass enclosures are best designed with a good software program, as tuning and enclosure changes can produce endless alignment variations viewable on your pc. Because these enclosures attenuate mid-range frequencies and higher at 12 dB/octave, they are good only for subwoofer duty.
Circular port diameters for drivers in vented and bandpass boxes:
Driver diameter (inches) |
Port diameter (inches) |
6 - 8 |
3 |
8 -10 |
4 |
10 -12 |
5 |
12 -15 |
6 |
These are general guidelines, and you may use a smaller size port if desired, especially for ported enclosures. Try and use the recommended values if possible, especially for bandpass. Recommended port values are for the minimizing of port turbulence and possible noise.
Port length for vented and bandpass (inches):
iR = port radius in inches (1/2 diameter)
Vb (Vf in bandpass) = box volume in cubic inches (multiply cubic ft by 1728 to find cubic in ).
Fb = tuned resonant frequency of box in Hz.
Lv = [1.463 (10^7) (R)^2 / (Fb^2) (Vb)] - (1.463) R |
If you want to use more than one port, you can solve for the equivalent cross-sectional area of the multiple ports that will equal a single, larger port. Two (or more) circular ports of diameter A and B (C, ect.) can be substituted for a single port with the larger diameter X:
X = ( A^2 + B^2 )^1/2(an exponent to 1/2 is the same as taking the square root) |
You may input as many ports as you wish into the equation. Just take the radius of X and input this into the port length equation. The final
length will apply to all ports being used, i.e. if you want to use 2 ports that are 3" in diameter, you will solve for a single equivalent port which would need to be 4.24" in diameter. Once you solve for the length of the 4.24" port, just make both 3" ports the same length to tune the box to Fb.
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