Thiele/Small parameters explained
A datasheet has twenty numbers on it and three of them decide your box. Here is what each one means, how they relate, and which ones to care about when.
The three that decide the box
Everything else on the datasheet is context. These three determine the enclosure:
| Parameter | Units | What it is |
|---|---|---|
| Fs | Hz | Free-air resonance — where the moving mass and the suspension resonate in open air. Roughly the lowest note the driver makes efficiently unaided. |
| Vas | L or ft³ | Equivalent compliance volume — the volume of air as stiff as the suspension. Big Vas means a loose suspension and a big box. |
| Qts | — | Total Q at resonance — how damped the driver is. Low Qts is tightly controlled; high Qts is loosely controlled and self-resonant. |
A sealed box is Vb = Vas / ((Qtc/Qts)² − 1). A ported box is Vb = 20 · Vas · Qts³·³. Neither formula contains the driver's diameter, its power rating, or its price.
The Q family
- Qes — electrical Q. Damping the motor provides, through back-EMF into the amplifier's low output impedance. Dominated by the magnet and voice coil: a strong motor gives low Qes.
- Qms — mechanical Q. Damping the suspension provides. Nearly always much larger than Qes, typically 3–10, so it contributes little.
- Qts — total Q. The two in parallel: Qts = (Qms · Qes) / (Qms + Qes). Because Qms is large, Qts is usually close to Qes.
| Qts | Character | Suits |
|---|---|---|
| Under 0.3 | Strong motor, tightly controlled, low efficiency at the bottom | Ported, horn |
| 0.3 – 0.4 | The usual subwoofer range | Ported, or a large sealed box |
| 0.4 – 0.6 | Moderately damped | Sealed, or a large ported box |
| Over 0.6 | Loosely controlled, self-resonant | Sealed only, or infinite baffle |
The one-number shortcut: EBP = Fs / Qes. Under about 50 leans sealed; over about 100 leans ported; between the two, either will work and the choice is about space and taste. It is a first sort, not a verdict — run both alignments and compare the curves.
The mechanical set
| Parameter | Units | Meaning and why it matters |
|---|---|---|
| Sd | cm² | Effective radiating area, measured to about the middle of the surround. With Xmax it sets the maximum air the driver can move. |
| Xmax | mm | Linear one-way excursion. Past it, distortion rises sharply. The real limit on how loud a sub plays at low frequencies. |
| Vd | L | Displacement volume, Sd × Xmax. The honest way to compare drivers of different sizes: a 10-inch with long travel can move more air than a shallow 12. |
| Mms | g | Moving mass — cone, coil, former and half the surround and spider, plus the air load. Heavy cones give low Fs and low efficiency. |
| Cms | mm/N | Suspension compliance — how easily the cone moves. Vas is Cms expressed as a volume of air. |
| Rms | kg/s | Mechanical losses in the suspension. Sets Qms. |
The relationships worth knowing:
Fs = 1 / ( 2π · √(Mms · Cms) ) Vas = ρc² · Sd² · Cms Vd = Sd · Xmaxρc² ≈ 1.4 × 10⁵ Pa at room temperature. Sd in m², Cms in m/N, gives Vas in m³.The electrical set
| Parameter | Units | Meaning |
|---|---|---|
| Re | Ω | DC resistance of the voice coil. Always below the nominal impedance — a "4 Ω" driver usually measures 3.2–3.6 Ω. |
| Le | mH | Voice coil inductance. Rolls off the top of the driver's range; largely irrelevant for a subwoofer. |
| BL | T·m | Motor force factor — magnetic flux density times coil length in the gap. The strength of the motor. High BL means low Qes. |
| Pe | W | Thermal power handling. A marketing number as often as an engineering one, and almost never the limit you hit first — Xmax usually is. |
| SPL / sensitivity | dB | Output at 1 W (or 2.83 V) at 1 m. Useful only when you know which of those two it means and what impedance the driver is. |
Why datasheets and reality disagree
Published parameters are measured on a new driver, often one sample, and they move:
- Break-in. A new suspension is stiff. After a few hours of use Fs typically falls 10–20% and Vas rises correspondingly. A box designed on new-driver figures ends up slightly wrong in a predictable direction.
- Sample variation. ±10% between units of the same model is normal, and ±20% is not unusual on inexpensive drivers.
- Temperature. A hot voice coil has higher Re, which raises Qes and therefore Qts, while the box stays the same size. Power compression is partly this.
Which is why a sealed box is the safer first build: a 15% volume error moves Qtc a little and nothing else. The same error in a ported box moves the tuning and can put the vent's unloading region somewhere you did not plan for.
Measuring them yourself
You need an audio interface, a known resistor and free software — the standard method drives the driver through a series resistor and measures the impedance curve. The peak gives Fs and Qms, the shape gives Qes, and a second measurement with a known added mass (or the driver in a known sealed box) gives Vas.
It takes about twenty minutes and it is worth doing whenever the box is expensive, the driver is cheap, or the datasheet is missing. Measure after break-in, not straight out of the carton.
Frequently asked questions
Which Thiele/Small parameters matter most for box design?
Three: Fs, Vas and Qts. Both the sealed and the ported formulas use only these.
Sd and Xmax decide how loud it can go rather than what size box it wants, and the rest of the datasheet is context.
What is a good Qts for a subwoofer?
It depends on the box, not on the number alone. 0.3–0.4 is the common subwoofer range and works ported or in a large sealed box. 0.4–0.6 suits sealed.
Below 0.3 the driver wants a ported or horn enclosure to be efficient; above 0.6 it is loosely controlled and really only works sealed or on an infinite baffle.
What does Vas mean and is a bigger Vas better?
Vas is the volume of air as stiff as the suspension — compliance expressed in units you can compare against a box. It is not better or worse, just bigger or smaller.
High Vas: loose suspension, more output per watt, large box. Low Vas: stiff suspension, small box, more power needed. Choose on the space you have.
Is Xmax the same as maximum excursion?
No. Xmax is the maximum linear excursion — how far the cone travels while the coil stays in the uniform part of the gap and distortion stays reasonable.
Beyond it the cone keeps moving, with rising distortion, until Xmech — where something hits a stop. Some datasheets quote a peak or mechanical figure as if it were Xmax, so check which one is meant.
Should I use the manufacturer parameters or measure my own?
Measure if the box is expensive to get wrong or the driver is cheap. Published figures come from a new driver, often one sample, and they drift: after break-in Fs typically falls 10–20% and Vas rises to match, with ±10% sample variation normal.
A sealed box tolerates that easily. A ported box does not — a volume error moves the tuning as well as the response.
Put the numbers to work
Type in Fs, Vas and Qts and watch the box, the curves and the cut list appear.
More calculators
Sealed box calculator
Solve the box from a target Qtc, and see where it rolls off.
Ported box calculator
Volume, tuning and vent, with the air-speed check people skip.
Subwoofer box calculator
Car and home subs, single or multiple drivers, with cabin gain in mind.
How to build a speaker box
From cut list to finished cabinet, and how to check it afterwards.