Port velocity calculator

The one identity worth memorising

A bass-reflex port is a plug of air whose mass, together with the springiness of the air in the box, forms a Helmholtz resonator. Fixing the tuning frequency fixes that mass. The standard result is that the port's effective length follows from its area:

L_eff = S_p · c² / (4π² · F_b² · V_b)

so length is proportional to area. Meanwhile the air speed in the port is the volume velocity divided by that same area:

v = U_p / S_p

so velocity is inversely proportional to area. Multiply the two and the area cancels completely:

v · L_eff = U_p · c² / (4π² · F_b² · V_b)

There is no S_p on the right-hand side. There is no diameter, no shape, and no port count. For a given driver, box volume, tuning and drive level, the product of port velocity and port length is a constant, and every port you could possibly build for that box lands somewhere on that one hyperbola. Halve the velocity and you have doubled the length. There is no third option and no clever geometry that escapes it.

This is why the usual advice — “use a bigger port if it chuffs” — is only half a sentence. A bigger port is quieter, and it is quieter in exact proportion to how much longer it now has to be. The real question was never what diameter to use. It is whether the length that buys you silence still fits in the box, and that is a question with a yes-or-no answer this page can give you before you cut anything.

Why the velocity every other calculator prints is too low

The formula in general circulation is the displaced-volume one:

v = S_d · X_max · 2πf / S_p

It says: the cone sweeps this much volume per second, all of it goes out through the port, divide by the port's area. The first half is fine. The second half is wrong, and near tuning it is wrong by a large factor.

Solve the four-element bass-reflex circuit and the ratio of port volume velocity to cone volume velocity comes out exactly:

U_p / U_d = 1 / (1 − (f/F_b)² + j·(f/F_b)/Q_L)

At f = F_b the real part vanishes and the magnitude is simply Q_L — the box's loss factor, typically about 7. The port moves seven times the volume the cone does. That is not a correction term; it is the entire reason a ported box works, and it is the reason the port is roaring at the exact frequency where the cone appears to be standing still. The displaced-volume formula ignores it and therefore understates port velocity at tuning by roughly a factor of Q_L.

The calculator prints both numbers so you can see the size of the gap on your own design. It also means the honest worst case is not set by excursion at all in most systems, but by amplifier power — which the displaced-volume formula never asks about.

The ceiling no amplifier can pass

Put the two results together at the tuning frequency, with the cone driven exactly to X_max, and you get a closed form for the highest port velocity a given driver and box can ever produce:

v_ceiling = Q_L · S_d · X_max · 2π F_b / S_p

This is the displaced-volume answer multiplied by Q_L, and it is a genuine ceiling: past it the cone is out of travel, so more amplifier buys distortion rather than air speed. It is worth calculating early, because if it lands below your chuffing limit the port simply cannot chuff, whatever you feed it, and you can stop thinking about port noise and go and worry about something else. If it lands well above, then the design is power-limited and the port noise you get is a choice you are making with the volume knob.

Where the velocity actually peaks

Not at F_b, quite. The ratio U_p/U_d peaks exactly at F_b, but the cone's own output is still climbing as frequency falls, so the product peaks a little below tuning — typically a few per cent, more with a lossy box. Once the excursion limiter is what is holding the drive back, the peak snaps to F_b itself, because that is the frequency at which the cone can be pushed to X_max while the port carries Q_L times as much. The calculator finds the maximum numerically rather than assuming F_b, and tells you which of the two regimes you are in.

How fast is too fast

Air in a port stops behaving linearly long before anything dramatic happens. Two mechanisms matter:

Chuffing is turbulence at the port ends. At the mouth, air that has been travelling as a neat column has to turn a sharp corner, separates, and sheds vortices — which radiate broadband noise you hear as a breathy huff on bass notes. It is worst at sharp-edged ends and it is why flares exist: a radius lets the flow stay attached at a higher speed.

Port compression is the loss that follows. Turbulent flow is dissipative, so the port stops being an efficient acoustic short circuit, output falls below what the model predicts, and the tuning drifts upward because the effective air mass is no longer the geometric one. You lose bass exactly when you asked for the most of it.

The conventional thresholds, all expressed as peak velocity:

These are conventions rather than measurements, and they are conventions about a peak, reached on transients, not about anything an average level would reveal. Treat them as the boundary of the region where the linear model you are using is still describing reality. Two things move the boundary in your favour: flaring, which is worth roughly a factor of 1.5 to 2, and content — a port that chuffs on a synthesised 35 Hz sine may never do it on music that has no sustained energy there.

The three walls around a port

A port has to satisfy three constraints at once, and they push in different directions. This is why port design feels harder than the arithmetic suggests.

Chuffing sets a minimum length. Because v × L is constant, demanding a velocity below your limit is exactly the same statement as demanding a length above L_min = (v·L) / v_limit. Nobody phrases it this way, and phrasing it this way is what makes the problem tractable.

The box sets a maximum length. A straight tube cannot be longer than the box's longest internal dimension, less clearance at both ends. You can buy some back by bending the port, running it along a wall, or folding it — at the cost of extra loss at the bend and a little extra effective length.

The port's own pipe resonance sets another maximum. A port is also an organ pipe, with its first mode at c / (2·L_eff). That resonance dumps unwanted midrange straight out of the port mouth, so it has to stay well above the passband — above the crossover point for a subwoofer, above a few hundred hertz for a woofer. A 20 cm port resonates around 850 Hz and is harmless. An 80 cm folded port resonates around 215 Hz and is not.

The window between those walls can be empty. When it is, the calculator says so instead of printing a number that cannot be built, and the ways out are all changes to something other than the port: raise the tuning, enlarge the box, accept less power, flare the ends, or give up on a port and use a passive radiator.

Two small ports instead of one big one

This is the most persistent piece of folklore in the subject, and the identity settles it in one line. Two ports of area S each behave as one port of area 2S: the acoustic masses are in parallel, so the length required per port is the length one 2S port would need. Two Ø 5 cm ports are, in every respect that matters, one Ø 7.07 cm port — same total area, same velocity, same length, same tuning.

So splitting a port into several buys you exactly nothing in velocity or length. What it does buy is diameter: four 5 cm holes fit on a baffle where one 10 cm hole will not, and four short tubes are easier to brace than one long one. That is a real reason, and it is a completely different reason from the one usually given. If you are adding ports in the hope of curing chuffing without lengthening anything, the physics is not going to cooperate.

The ways out when nothing fits

Flare the ends. Cheapest fix, roughly 1.5× to 2× the tolerable velocity, which is 1.5× to 2× off the required length. A radius of about a quarter of the diameter gets most of the benefit; a full trumpet flare gets the rest.

Use a slot port. A slot formed by the box walls can run the full internal height or depth, so it can be far longer than any tube you could stand up inside the same box, and its area is set independently by the gap. The trade is friction: a very thin slot has a lot of wall area for its cross-section, so losses rise and the boundary layer starts to matter. Keep the aspect ratio under about 10:1 and the narrow dimension above about 13 mm.

Raise the tuning. The constant falls steeply as F_b rises — the length term alone carries 1/F_b² — so a few hertz of tuning is worth a surprising amount of port. Going from 30 Hz to 34 Hz in the calculator's default box cuts the required length by about a sixth.

Use a bigger box. The constant scales as 1/V_b. This is the expensive answer and usually the one you already rejected.

Give up the port. A passive radiator has the same tuning behaviour with no aperture at all, so it cannot chuff and cannot have a pipe resonance. It costs more than a cardboard tube and needs its own mass tuning, and for a small box asked to go deep and loud it is often the only honest answer.

What this model does and does not include

It is the standard lumped-element fourth-order bass-reflex model, with box losses collected into a single Q_L in series with the port mass, driven from a constant-voltage source scaled through the driver's quoted sensitivity. That is enough to get volume velocities right in and around the passband, which is where port velocity lives.

It does not model: port compression and the tuning shift it causes at high level (so the velocities it reports at the top of the range are, if anything, optimistic); the driver's own nonlinearity as it approaches X_max; standing waves inside the box; or thermal power compression, which after a few seconds of real programme material can quietly remove several decibels of everything. Q_L itself is the least knowable input on the page — it is a single fudge for several distinct loss mechanisms and it is rarely measured — so treat the velocity figure as accurate to the tens of per cent, not to the decimal place the calculator prints. What is exact, and worth trusting, is the v × L relationship: that one falls out of the geometry and holds whatever Q_L turns out to be.

FAQ

My port came out longer than the box. Now what?

In order of how much they cost you: flare the ends, fold the port along a wall, switch to a slot port formed by the box walls, raise the tuning a few hertz, or fit a passive radiator. Adding a second port of the same diameter will not help — see above.

Does the velocity limit apply to peak or average level?

Peak. The figures on this page are peak velocities from a sine at the stated power, which is the convention the 17 m/s rule of thumb was written for. Music has a crest factor of 10 dB or more, so a system whose peaks touch the limit is spending very little time near it.

Should I use the amplifier's rated power or what I actually listen at?

Both, and the difference is informative. Rated power tells you what happens when someone else turns it up; typical listening power tells you what you will live with. If the port is fine at one and terrible at the other, the design decision is about how much protection you want, not about the port.

Why does the velocity fall below tuning in the chart?

Because the excursion limiter is holding the cone at X_max. Below F_b the box unloads the cone and the excursion demanded rises very steeply, so the model caps the drive there — which is precisely what a high-pass filter does in a real system, and precisely what a system without one fails to do. If you have no subsonic filter, the driver goes past X_max down there and the curve is optimistic.

Does port velocity matter in a sealed box?

There is no port, so no. A sealed box trades the port's extra half-octave of extension for the complete absence of this entire class of problem — no chuffing, no pipe resonance, no tuning to get wrong, and a gentle 12 dB/octave rolloff that is far kinder to a driver below cutoff. If the port this page recommends will not fit, the sealed alignment is not a defeat.