Formula
Gross internal volume is the inside of the six panels. Each wall takes its thickness off both sides, so the internal size is (W − 2t) by (H − 2t) by (D − 2t). A double-thick front baffle takes one more thickness off the depth. One cubic foot is 1,728 cubic inches and 28.3168 litres. Net volume subtracts the driver displacement, the port displacement, and a bracing allowance. The bracing allowance is a percent of the gross internal volume. Three to five percent is a usual planning figure when you have not drawn the braces yet.
Vgross = (W − 2t)(H − 2t)(D − 2t)
Vnet = Vgross − Vdriver − Vport − Vbrace
1 ft³ = 1,728 in³ = 28.3168 L
Thiele-Small parameters, sealed and ported
Fs is the free-air resonance, Qts is the total Q, and Vas is the volume of air with the same compliance as the suspension. Qes is optional. EBP is Fs / Qes. Under about 50 the driver suits a sealed box. Over about 90 it suits a ported box. The band in between can go either way.
A sealed box follows Richard Small’s closed-box relations from 1972. Alpha is Vas / Vb. Qtc is Qts times the square root of alpha plus one. Fc is Fs times Qtc / Qts. Rearranged, the net volume for a target Qtc is Vas / ((Qtc / Qts)² − 1), and that only exists when Qtc is higher than Qts. F3, the frequency where the response is at 1/√2, is Fc times the square root of ((a + √(a² + 4)) / 2), with a = 1/Qtc² − 2. At Qtc 0.707 that F3 lands on Fc. You can run it backwards: type a net volume and read Qtc, Fc, and F3.
Qtc = Qts √(Vas/Vb + 1)
Vb = Vas / ((Qtc/Qts)² − 1)
Fc = Fs · Qtc / Qts
Qtc 0.577 is a larger, gentler box. Qtc 0.707 is the Butterworth starting point, flat through the passband, and it is the default here. Qtc 1.0 is a smaller box with a hump: more output near the corner and less extension below it. The curve on this page is that second-order high-pass. It is the textbook shape, not a measurement in your car.
A ported box on this page is D. B. Keele’s QB3 starting point from the Journal of the Audio Engineering Society, 1981. Vb is 15 × Qts^2.87 × Vas. Fb is 0.42 × Fs × Qts^−0.90. F3 is 0.26 × Fs × Qts^−1.40. You can override Vb or Fb. Once you do, the Keele F3 no longer belongs to that box, so the page stops printing it. Qts above about 0.5 is a poor candidate for this alignment. Bandpass enclosures are out of scope. Either way, model the driver in something like WinISD before you buy wood. This is a starting point.
Subwoofer port length
The port is a Helmholtz resonator. With the speed of sound at 343 m/s, the tuned length before the end correction is c² times the total port area, divided by 4π² Fb² Vb. The end correction comes off that length. A round port uses its inside diameter. A slot uses the equivalent diameter 2 √(area / π). One flanged end and one free end take 0.732 diameters. Both ends flanged take 0.85 diameters. Several identical ports share the tuning, so the area in the formula is the sum, and each port is cut to that same length.
Lv = c² Sp / (4 π² Fb² Vb) − k d
k = 0.732 or 0.85
v = 2 π Fb Sd Xmax / Sp
Peak port velocity is 2π Fb Sd Xmax divided by the total port area. Above about 17 m/s the port usually starts to make noise. Car-audio builds often live with 25 to 30 m/s. A length that is not positive, or a port longer than the internal depth, is reported as an error: the tube will not tune, or it will not fit as a straight port. A sub box calculator is this whole page. The outside-dimension part is what people mean by a speaker box calculator. The volume that remains after the parts go in is the subwoofer box volume.
Cabin gain, materials, and sealing
A car cabin raises the low frequencies as the wavelength gets long compared with the cabin. The rise is real and it is not a single number. A home room does not do the same thing. Do not add a cabin-gain curve that this page does not have. Use ¾ inch MDF, or a stiffer plywood if the box is large, glue and screw the joints, and seal every seam. Brace the panels that can flex. A leaking box is a different alignment than the one you calculated.
Worked examples
Outside 20 × 15 × 15 in, ¾ in walls. Gross internal volume is 3,371.6 in³, 1.951 ft³, 55.25 L.
Sealed, Fs 25 Hz, Qts 0.40, Vas 100 L, Qtc 0.707. Net volume is 47.08 L (1.663 ft³). Fc and F3 are both 44.19 Hz and 44.19 Hz.
The same driver in 60 L. Qtc is 0.653, Fc is 40.82 Hz, and F3 is 44.47 Hz.
Ported QB3, same driver. The starting point is 108.1 L, tuned to 23.95 Hz, with F3 at 23.44 Hz.
One 10 cm round port, 50 L, 35 Hz, one flange and one free end. The cut length is 30.9 cm.
Reference
The five checks for this page. Ported F3 is Keele’s, and it moves as soon as you override Vb or Fb.
| Case | Result |
|---|---|
| 20 × 15 × 15 in, 0.75 in walls | 3,371.6 in³ · 1.951 ft³ · 55.25 L |
| Sealed, Qtc 0.707 | 47.08 L · Fc 44.19 Hz · F3 44.19 Hz |
| Sealed, 60 L | Qtc 0.653 · Fc 40.82 Hz · F3 44.47 Hz |
| Ported QB3 | 108.1 L · Fb 23.95 Hz · F3 23.44 Hz |
| 10 cm port, 50 L, 35 Hz | 30.9 cm |
Questions
How big a box does a 12-inch sub need?
The spec sheet wins. A 12-inch driver is often planned somewhere around 0.75 to 1.5 cubic feet sealed, or about 1.5 to 2.75 cubic feet ported, and those spans are only a place to start. Vas, Qts, and the manufacturer’s recommended net volume replace them.
Should a subwoofer box be sealed or ported?
Sealed is smaller and rolls off gently. Ported plays lower for the same driver when the tuning is right, and it unloads below the tuning. EBP, which is Fs divided by Qes, is a hint: under about 50 favors sealed, over about 90 favors ported, and the middle can go either way. Qts above about 0.5 is a poor fit for the ported starting point on this page.
What is net volume?
Net volume is the air left after the driver, the port, and the bracing. Gross internal volume is only the inside of the panels. A subwoofer box volume calculator that stops at the outside dimensions is still counting the wood you cut away and the parts you have not put in yet.
How long should the port be?
Length comes from the net volume, the tuning frequency, and the port area, minus an end correction. A bigger port, or more ports, has to be longer to hold the same tuning. This subwoofer port calculator uses 0.732 diameters when one end is flanged and one is free, and 0.85 diameters when both ends are flanged.
What tuning frequency is usual for a car sub?
Many car boxes are tuned around 30 to 35 Hz. The cabin adds low-frequency gain, so a tuning that looks high on a datasheet can still sound deep in a car. Start from the manufacturer’s recommended Fb. This page does not model the cabin.
Does the port count toward the box volume?
Yes. The air inside the port is not part of the net box. When the box is ported, this page subtracts that displacement from the gross internal volume. Thick port walls displace a little more. Measure them if you need that last bit.
Why doesn’t this match the manufacturer’s box?
They may use a different end correction, include the port wall, round the panels to a cut sheet, or model the car. These figures are a starting point. Check them in a modelling program such as WinISD before you cut.
Sources
- Richard H. Small, “Closed-Box Loudspeaker Systems,” Journal of the Audio Engineering Society, 1972. Qtc, Fc, and the volume for a target Qtc.
- D. B. Keele, Jr., “A New Set of Sixth-Order Vented-Box Loudspeaker System Alignments,” Journal of the Audio Engineering Society, 1981. The QB3 starting point used here.
- Kinsler, Frey, Coppens, and Sanders, Fundamentals of Acoustics. Helmholtz resonator and the flanged end correction. This page uses 0.732 diameters for one flanged end and one free end, and 0.85 diameters for both ends flanged, with c = 343 m/s.
- These are design starting points. Verify the cut list in a modelling program such as WinISD. A manufacturer’s recommended net volume and tuning replace every number on this page.