Thiele/Small parameters explained: what each number means for your box

Thiele/Small parameters are a handful of measurements that describe how a woofer behaves at low frequencies. Fs, Qts and Vas decide what box suits the driver; the rest tell you how loud and how far it can play.

What Thiele/Small parameters are

In the early 1970s, Neville Thiele and Richard Small showed that a woofer in a box can be modelled as a simple electrical and mechanical circuit. Feed that model a few numbers and you can predict the bass response of any sealed or ported box before you cut wood. Those numbers are the Thiele/Small (T/S) parameters, and every box calculator, including the BassDesign calculator, runs on them.

They fall into two groups: small-signal parameters that set the frequency response, and large-signal parameters that set limits on output.

Small-signal parameters

Fs: free-air resonance

The frequency at which the moving mass and suspension stiffness resonate with the driver hanging in free air, in Hz. Lower Fs generally means the driver can reach lower in a reasonably sized box. Typical subwoofers sit between 20 and 40 Hz.

Qms, Qes and Qts: the damping numbers

Q describes how strongly the resonance at Fs is controlled. Lower Q means more damping.

• Qms is mechanical damping from the suspension losses. Usually large, 3 to 10.
• Qes is electrical damping from the motor (magnet and voice coil) working against the amplifier. Usually 0.3 to 0.7, and it dominates.
• Qts is the total, combining both.

Qts is the single most important number for choosing a box. Low Qts (below about 0.4) drivers are well damped and suit ported boxes. Higher Qts (0.5 and up) drivers tend to prefer sealed boxes, or even free-air and infinite-baffle mounting.

Vas: equivalent compliance volume

The volume of air that has the same stiffness as the driver's suspension, in litres or cubic feet. A floppy suspension has a large Vas. Vas scales the box: in a sealed box, Qtc = Qts · sqrt(1 + Vas/Vb), so for the same Qts a driver with double the Vas needs double the box for the same alignment. See the box volume guide for the full sealed and ported maths.

Re and Le

Re is the DC resistance of the voice coil in ohms, a little below the nominal impedance (a "4 ohm" sub often reads 3.2-3.6 Ω). It sets how much power the amp delivers. Le is voice-coil inductance in millihenries; it causes the impedance to rise with frequency. It matters little in the sub-bass range but affects how a driver behaves higher up.

BL, Mms and Sd

BL is the motor strength, magnetic flux density times the length of wire in the gap, in tesla-metres. Mms is the moving mass including air load, in grams. Sd is effective cone area, in cm² or m². These are the "building blocks" from which Fs, Qes and Vas are derived. Strong BL with modest mass gives a low Qes; a large Sd moves a lot of air per millimetre of travel.

Large-signal parameters

Xmax

The maximum one-way linear excursion of the cone, in millimetres. Beyond it, distortion rises quickly. Multiply by Sd to get displaced volume, Vd = Sd · Xmax, the best single predictor of how much bass a driver can produce at low frequencies. A 12-inch with Sd = 480 cm² and Xmax = 12 mm displaces 576 cm³; a driver with half the Vd is roughly 6 dB less capable at the bottom end, all else equal.

Pe

Rated thermal power handling, in watts RMS. It describes how much heat the voice coil can survive, not how much power is safe at every frequency. In a ported box below tuning, a driver can exceed Xmax with a fraction of its rated power.

How the parameters pick the box

The quickest screen is the efficiency bandwidth product.

From there, the alignment formulas take over. For a sealed box you choose a target Qtc (0.707 is the flattest, Butterworth) and solve Vb = Vas / ((Qtc/Qts)² − 1). For a ported box the classic (Keele) QB3-style starting point is Vb ≈ 15 · Vas · Qts^2.87 with Fb ≈ 0.42 · Fs · Qts^-0.9. The sealed vs ported guide walks through the decision in more depth.

Xmax and Sd then tell you whether the chosen box can actually play loud. Two drivers with identical Fs, Qts and Vas give the same response shape, but the one with more Vd will reach higher output before bottoming, and needs a bigger port to keep air velocity down (see the port noise guide).

Worked example: checking a datasheet

Suppose a datasheet lists Fs = 30 Hz, Qms = 5.2, Qes = 0.45, Qts = 0.41, Vas = 2.1.

First, the Q consistency check:

0.45 × 5.2 / (0.45 + 5.2) = 2.34 / 5.65 ≈ 0.414, which matches the listed 0.41. Good.

Next, EBP = 30 / 0.45 ≈ 66.7, in the "either" zone, so both a sealed and a ported box are viable.

Finally, the units of Vas. A value of 2.1 with no unit is suspicious. As litres it would be a tiny suspension for a 12-inch sub. As cubic feet it is 2.1 × 28.317 ≈ 59.5 L, which is typical. Always confirm, because entering it in the wrong unit changes every box size by a factor of 28.

Spotting datasheet typos

• Vas in ft³ vs L: a factor of 28.317 between them. Subwoofer Vas values usually fall between 20 and 150 L (0.7-5.3 ft³). A 12-inch with Vas = 2 L or 200 ft³ is a unit error.
• Qts does not match Qes and Qms: run the formula above. A mismatch of more than a few percent means one of the three is wrong, or they came from different samples.
• Sd in the wrong unit: cm² vs m² vs in². A 12-inch sub is about 450-520 cm² (70-80 in²).
• Xmax that is really Xmech: some sheets list the mechanical damage limit. If "Xmax" is suspiciously large, look for a separate linear figure.
• Dual voice coil confusion: Re, Qes and BL can be quoted per coil or with coils wired in series or parallel. Qts and Fs stay the same, but power and impedance calculations do not.
• Fs, Vas and Mms that cannot coexist: Fs depends on Mms and the suspension compliance implied by Vas and Sd. If one changes wildly between revisions of a datasheet, ask the manufacturer.

When in doubt, measure. An inexpensive impedance-measurement jig gives you Fs, Qes, Qms and Re, and with a known added mass, Vas too. Parameters also drift as a suspension breaks in, typically lowering Fs and raising Vas slightly.

Once your numbers pass these checks, enter them in BassDesign and let the simulation do the rest. It is free, needs no sign-up and runs entirely in your browser.