Max SPL from Displacement
Estimate the displacement-limited maximum output of one or more subwoofers across 10–100 Hz.
Inputs
Use Xmech or ‘usable’ Xmax for absolute limits.
Added subs = more headroom
| Subs | Vd | @ 20 Hz | @ 31.5 Hz | @ 63 Hz |
|---|---|---|---|---|
| 1 | 0.8 L | 98.3 dB | 106.1 dB | 118.2 dB |
| 2 | 1.6 L | 104.3 dB | 112.2 dB | 124.2 dB |
| 3 | 2.3 L | 107.8 dB | 115.7 dB | 127.7 dB |
| 4 | 3.1 L | 110.3 dB | 118.2 dB | 130.2 dB |
| 6 | 4.7 L | 113.8 dB | 121.7 dB | 133.7 dB |
| 8 | 6.2 L | 116.3 dB | 124.2 dB | 136.2 dB |
Each doubling of drivers = +6 dB when they sit close together.
How it works
A subwoofer is a volume pump. At low frequencies, how loud it can play is not limited by its power rating, but by how much air the cone can move before it hits its mechanical or linear limits. That quantity is the peak displaced volume Vd = Sd × Xmax.
Vd = Sd · Xmax · N p_pk = ρ · (2πf)² · Vd / (Ω · r) SPL = 20·log₁₀( p_pk / √2 / 20 µPa )
where ρ = 1.18 kg/m³, Ω is the solid angle the sound radiates into (4π in free air, 2π on the floor, π against a wall, π/2 in a corner), and r is the distance. The key insight is the f² term: maximum output falls 12 dB per octave as frequency decreases. To play a note an octave lower at the same level you need four times the displacement.
That is why 4 × 12″ subs beat 1 × 18″: the same Vd comes from more cone area with less excursion. Compare this limit with the amp-limited SPL from the SPL Calculator, whichever is lower is what you’ll actually get. Ported boxes and cabin gain can cheat in a narrow range, but nothing beats displacement.