Subwoofer tools.
DRIVERS & OUTPUT / THE TOOLKIT

Excursion & SPL.

Estimate the ideal compact-source SPL from one-way excursion, or work backward from a target level. This is a displacement limit, not a promise of clean output.

01 / THE INPUTS
Calculation mode
Driver & output
Hz
Radiation
Air & conventions
m/s
kg/m3
02 / THE RESULTS
Ideal displacement-limited output
101.6dB SPL
One-way volume displacement
0.500L
Peak-to-peak volume displacement
1.000L
RMS pressure at listening point
2.399Pa

Ideal output at constant one-way excursion

LOG FREQUENCY
Ideal output at constant one-way excursion: SPL (dB) against frequency in hertz.78.3390.41102.48114.55126.63138.7102050100200SPL (dB)Frequency (Hz)

Not a clean-output or power-handling guarantee. This excludes port/radiator output, room effects, heating, and nonlinear driver behavior.

Read this result with its assumptions.

1 coherent driver at 1 m in ideal half-space. Xmax means one-way peak excursion.

Units & assumptions

Your calculations run in this browser. No account needed.

03 / UNDER THE HOOD

The math, in plain sight.

How much sound can displacement tell you about?

Displacement, velocity, and pressure

For N identical drivers moving coherently in phase, X is one-way peak displacement. It is not peak-to-peak travel. The pressure estimate assumes an acoustically compact source at the listening position.

Vd,peak=NSdX,Vd,peak ⁣ ⁣ ⁣−to ⁣ ⁣ ⁣−peak=2NSdXV_{d,\mathrm{peak}}=NS_dX,\qquad V_{d,\mathrm{peak\!\!\!-to\!\!\!-peak}}=2NS_dX
URMS=ωNSdX2U_{\mathrm{RMS}}=\frac{\omega NS_dX}{\sqrt2}
pRMS≈ρωURMSΩr=ρω2NSdX2 Ωrp_{\mathrm{RMS}}\approx\frac{\rho\omega U_{\mathrm{RMS}}}{\Omega r}=\frac{\rho\omega^2NS_dX}{\sqrt2\,\Omega r}
Lp=20log⁡10(pRMS20×10−6 Pa)L_p=20\log_{10}\left(\frac{p_{\mathrm{RMS}}}{20\times10^{-6}\ \mathrm{Pa}}\right)

Work backward from an SPL target

One driver with 500 cm2 area and 10 mm one-way excursion has 0.50 L one-way displacement. At 30 Hz and 1 m in ideal half-space, the estimate is approximately 101.6 dB SPL.

ptarget=20×10−610Lp/20 Pap_{\mathrm{target}}=20\times10^{-6}10^{L_p/20}\ \mathrm{Pa}
Xrequired≈2 Ωrptargetρ(2πf)2NSdX_{\mathrm{required}}\approx\frac{\sqrt2\,\Omega r p_{\mathrm{target}}}{\rho(2\pi f)^2NS_d}

This excludes port and passive-radiator output, thermal limits, motor and suspension nonlinearities, and room effects. At high frequency or in a room, compactness and coherent-addition assumptions can fail.