Sealed box calculator

A sealed box is one number — the volume — and that number follows directly from how damped you want the result. Pick a target Qtc, and the box, the system resonance and the roll-off all fall out of it.

The formula

Sealing a driver into a box adds an air spring in parallel with the suspension. That raises resonance and raises Q by the same factor:

α = Vas / Vb Qtc = Qts · √(1 + α) Fc = Fs · √(1 + α)α is the compliance ratio. Qtc is the system Q; Fc is the system resonance.

Which rearranges into the thing you actually want — the box volume for a chosen Qtc:

Vb = Vas / ( (Qtc / Qts)² − 1 )Vas and Vb in the same units. If Qts is already above your target Qtc, no box can get there.

And the −3 dB point follows from Qtc and Fc alone:

u = [ (1/Qtc² − 2) + √( (1/Qtc² − 2)² + 4 ) ] / 2 F3 = Fc · √uA second-order high-pass. Below F3 it falls at 12 dB per octave, forever.

Choosing Qtc

0.707 is the right default for a home subwoofer or a monitor. Go to 0.8–1.0 for a car, where you want a little extra weight before the cabin takes over and where box space is expensive. Go below 0.707 only if you have room and want the cleanest transient response you can get — a kick drum in a Qtc 0.577 box stops when the drum does.

Worked example

Take a driver at Fs = 28 Hz, Vas = 60 L, Qts = 0.42, and aim for Qtc = 0.707.

Vb = 60 / ( (0.707 / 0.42)² − 1 ) = 60 / ( 2.833 − 1 ) = 60 / 1.833 = 32.7 L net α = 60 / 32.7 = 1.83 Fc = 28 · √(1 + 1.83) = 28 · 1.682 = 47.1 Hz F3 = Fc = 47.1 Hz (Qtc = 0.707, so F3 = Fc)

So: a 32.7-litre net box, −3 dB at 47 Hz, falling 12 dB per octave below that. In a car, cabin gain will flatten that out a long way further down. In a room it will not, which is why the same driver ends up in a bigger box indoors — Qtc 0.577 here gives 47 litres and F3 of 46 Hz, barely different at −3 dB but noticeably deeper at 30 Hz.

Net volume, not gross

Vb is the air the driver sees. Everything inside the box that is not air has to be added back on top when you work out the external dimensions:

• The driver — the basket and magnet displace 1–4 litres on a typical sub.
• Bracing — a window brace is a litre or two.
• The terminal cup — a few hundred millilitres.
• The panels themselves — 18 mm walls take 10–15% off the outside volume.

The calculator's cabinet tab works both figures out and gives you external dimensions and a cut list from the net volume you asked for, so you are never converting by hand.

Stuffing

Polyester fibre in a sealed box does two useful things: it damps internal standing waves in the upper bass, and it slows the air's thermal exchange so the compression becomes closer to isothermal than adiabatic. The second effect makes the box behave as if it were larger — typically 10–20% with a moderate fill, occasionally more.

Practically: fill the box loosely, about 0.5–1.0 kg per 30 litres, and do not pack it hard. Do not design around the gain — treat it as a bonus that lets you nudge Qtc down slightly after the box is built, and leave the volume calculation alone.

Frequently asked questions

What Qtc should I aim for in a sealed box?

0.707 is maximally flat and the right default for home use: the −3 dB point sits exactly at system resonance, with no peak.

0.8–1.0 is common in car audio, where a small rise adds weight and box space is expensive. 0.577 gives the best transient response but needs a noticeably bigger box. Above about 1.1 the response peaks audibly and bass starts to sound one-note.

Does a smaller sealed box damage the driver?

No — the opposite. A smaller box is a stiffer air spring, which restricts cone travel for the same input. Sealed boxes get mechanically safer as they get smaller.

The cost is thermal rather than mechanical — you need more power for the same output — plus the higher Qtc that comes with it.

How much polyfill should I put in a sealed box?

Loosely, roughly 0.5–1.0 kg per 30 litres, spread through the box rather than stuffed into the corners. That damps internal standing waves and makes the box act as if it were 10–20% larger.

Build to the calculated volume and treat stuffing as fine-tuning afterwards. Packing it hard restricts air movement and does more harm than good.

Why is my sealed box F3 higher than the driver Fs?

Because sealing a driver into a box always raises its resonance. The air is a spring in parallel with the suspension, so Fc = Fs · √(1 + Vas/Vb) — always higher than Fs.

The only way down is a bigger box, and the limit is an infinite baffle, where Fc = Fs. If you need output below Fs, you want a ported or bandpass alignment, not a bigger sealed one.

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