Acoustic Calculators — SBIR, Room Modes, Sensitivity and Power
Acoustic calculators
Nine tools in three sections — placement and room, loudspeaker and system, interaction and measurement — plus a reference and auxiliaries section, to apply the report's formulas to a specific case. Each result carries a CALCULATED label and its scope note: they are calculations under declared assumptions, not measurements.
It is a quick way to apply the formulas from Part III of the report to your specific case, avoiding unit errors (the most common: 1 W vs. 2.83 V). It is not a consultant telling you where to place loudspeakers, nor a substitute for measuring your room. The three inputs a consultant would ask for (dimensions, loudspeaker type, listening distance) do not contain the information that determines the real response: where the door, window and furniture are, whether the room is symmetrical about the listening axis, whether there is treatment, what the loudspeaker's real directivity is, and where the listening position is. That is why each tool here illuminates relationships and refers back to the report; none prescribes actions.
Note on numeric fields: they accept both a decimal point and a decimal comma (4.8 or 4,8). The range warnings shown next to the fields are informative, not enforced by the browser.
TOOLS
Nine tools organised into three sections: placement and room (SBIR + boundary gain, modal explorer), loudspeaker and system (sensitivity with dB converter, power/SPL, damping factor and Q_res/BW/τ_res) and interaction and measurement (delay/phase/summation, critical distance and absorption and time window → frequency resolution). A final reference and auxiliaries section keeps the elementary conversions (ms ↔ m, λ ↔ f ↔ T) and the target curve slope illustration. All outputs are CALCULATED: they are not measurements.
Section I · Placement and room (2)
SBIR and boundary gain share the distance d to the front wall and the boundary type. The modal explorer completes the room's landscape. The distance to the wall and the room dimensions determine the frequencies that will be affected.
1 · SBIR and boundary gain
The distance from the woofer to the front wall and the boundary type determine the first SBIR null, the first constructive reinforcement and the maximum boundary gain. Boundary gain and SBIR interference are related, but they are not equivalent quantities: they describe different effects of the same proximity to the boundary. For axial modes, see the 2 · Explorer.
CALCULATED SBIR: point-source model, flat infinite wall, perpendicular incidence, c = 343 m/s. First null at f = c/(4d); first constructive reinforcement at f = c/(2d) (ideal frequency; the amplitude of the reinforcement depends on the reflection coefficient and on the geometry). d must be the acoustically relevant distance between the radiation centre and the reflective surface, not necessarily the distance to the cabinet front face. The frequency and depth of the real null also depend on listener position, incidence angle and other surfaces. Boundary gain: idealised upper bounds of 0 / +6.02 / +12.04 / +18.06 dB for 0/1/2/3 ideal reflective boundaries. The +18 dB bound (eighth-space) is a theoretical limit that is not reached in practice: it would require three infinite rigid walls with the loudspeaker in a perfect corner. In a real room, the effective value is lower due to absorption, finite wall size and furniture. Boundary gain and SBIR interference are related, but they are not equivalent quantities: they share the geometry of the boundary and the distance d, but they describe distinct phenomena. The specific result in a given room depends on the geometry, the surfaces and the listening position, and is not predicted by the simplified model. Developed in Part III.1.2 of the report and Annex D.12.
2 · Modal axial explorer and Schroeder frequency
Enter your room dimensions and estimated T60. The tool shows the first axial modes (not tangential or oblique), marks modes by zone (modal / statistical), lets you switch between the dimension view (3×3) and the frequency-ordered view (12 modes), and links to the report sections that address your case. It does not recommend loudspeaker or listener positions.
Axial mode table views
| Dimension | n = 1 | n = 2 | n = 3 |
|---|---|---|---|
| Length | 35.7 Hz | 71.5 Hz | 107.2 Hz |
| Width | 47.6 Hz | 95.3 Hz | 142.9 Hz |
| Height | 68.6 Hz | 137.2 Hz | 205.8 Hz |
Each row decomposes one room dimension; each column is the axial mode order.
| # | Mode | Frequency | Zone |
|---|---|---|---|
| 1 | Length n=1 | 35.7 Hz | Modal zone |
| 2 | Width n=1 | 47.6 Hz | Modal zone |
| 3 | Height n=1 | 68.6 Hz | Modal zone |
| 4 | Length n=2 | 71.5 Hz | Modal zone |
| 5 | Width n=2 | 95.3 Hz | Modal zone |
| 6 | Length n=3 | 107.2 Hz | Modal zone |
| 7 | Height n=2 | 137.2 Hz | Modal zone |
| 8 | Width n=3 | 142.9 Hz | Modal zone |
| 9 | Length n=4 | 142.9 Hz | Modal zone |
| 10 | Length n=5 | 178.6 Hz | Modal zone |
| 11 | Width n=4 | 190.6 Hz | Modal zone |
| 12 | Height n=3 | 205.8 Hz | Statistical zone |
Blue = below fs (modal zone; an indicative graphical classification, not an exact physical boundary). With the checkbox active, yellow = inside the 70–90 Hz band of the X3 boost described in Part II.1 of the report.
First SBIR null at different distances
| Distance to wall | First null | Note |
|---|---|---|
| 0.30 m | 285.8 Hz | — |
| 0.50 m | 171.5 Hz | Proximity indication: Length n=5 (178.6 Hz) |
| 0.80 m | 107.2 Hz | Proximity indication: Length n=3 (107.2 Hz) |
| 1.00 m | 85.8 Hz | — |
| 1.50 m | 57.2 Hz | — |
| 2.00 m | 42.9 Hz | Proximity indication: Width n=1 (47.6 Hz) |
Proximity indication = difference smaller than the declared tolerance: max(5 Hz, 6 % of the mode frequency). The match is searched only among modes below fs, where modal behaviour is physically dominant; above fs the modal interpretation loses its meaning. Frequency proximity does not imply effective interference: the mode and the SBIR null may reinforce, weaken, or prove inaudible depending on the listening position.
What the report says about your case
CALCULATED Calculations under simplified models (rigid rectangular room, point-source SBIR, c = 343 m/s). The Schroeder frequency of the example is a transition estimate, not an abrupt physical boundary. In small rooms the mode distribution is irregular. The report summaries link to the relevant sections.
Section II · Loudspeaker and system (4)
Sensitivity with dB converter, power/SPL, damping factor and Q_res ↔ BW ↔ τ_res. The loudspeaker and the electrical chain.
3 · Sensitivity and dB converter
Two tabs that share the underlying idea: the reference matters. Without declaring the reference, comparing figures produces errors of 3 to 6 dB, of the same order as many differences discussed as audible.
dB at 2.83 V/1 m = dB at 1 W/1 m + 10·log₁₀(8/R). The conversion assumes a resistive load; a real loudspeaker's impedance varies with frequency. Choose the reference in which the manufacturer's figure is published and the page calculates the other.
CALCULATED Nominal equivalence. It does not automatically convert a real measurement into an equivalent one: a real loudspeaker's impedance varies with frequency. Comparing figures without declaring the reference produces errors of 3 to 6 dB. Table and context in Annex B of the report.
Enter a value and its unit. The table shows all equivalences. Reference: dBu and dBm use √0.6 = 0.7746 V, so 0 dBu = 0 dBm at 600 Ω. dBFS requires a declared reference (0 dBFS = X dBu / X Vrms); without that reference it is not converted to SPL or voltage.
| Quantity | Equivalence |
|---|---|
| dBu | 0.00 dBu |
| dBV | −2.22 dBV |
| dBm @ 600 Ω | 0.00 dBm @ 600 Ω |
| Vrms | 0.7746 V |
| Vpeak | 1.0954 V |
| Vpp | 2.1909 V |
CALCULATED Voltage conversion (dBu, dBV, Vrms, Vpeak, Vpp) and power (dBm referred to 600 Ω). dBu = 20·log₁₀(Vrms/0.7746). dBV = 20·log₁₀(Vrms/1.0). dBm (600 Ω) = 20·log₁₀(Vrms/0.7746). With √0.6, 0 dBu = 0 dBm exactly. The dBu ↔ dBm equivalence is only valid at 600 Ω; for other load impedances it does not hold. dBFS is not included: it is a digital unit that requires declaring the converter reference (0 dBFS = X dBu / X Vrms). Developed in Annex B of the report.
4 · Power and SPL
SPL at 1 W and d metres = sens − 20·log₁₀(d). Average power = 10^((target SPL − SPL at 1 W − acoustic correction)/10). Peak power = average power × 10^(crest/10). The acoustic correction adds stereo gain (+3 dB) and room gain (variable by room). The result is power per channel, not the system total.
CALCULATED Idealised exercise under the declared assumptions. The acoustic correction is not a substitute for measuring; it is an approximation to estimate order of magnitude. The +7 and +10 dB scenarios are illustrative hypotheses, without a normative source: real room gain depends on the room, the listening position and the inter-channel correlation, and is not constant across the band. They are not guarantees of reinforcement. At peak levels above ~300 W, excursion and thermal compression limit before available power; the 300 W threshold is a warning signal, not a universal physical limit. The values are not amplifier specifications. For PA systems with multiple cabinets, arrays or ceiling coverage, see other tools. Developed in Annex B of the report.
5 · Damping factor and response variation
Damping factor: DF = Zload / Zout. Response variation with load impedance: Δ(dB) = 20·log₁₀[(Zmax/(Zseries+Zmax)) / (Zmin/(Zseries+Zmin))], with Zseries = Zout + Rcable. Resistive model. The result estimates the effect of series resistance on the response, not the complete response of a real loudspeaker.
CALCULATED Resistive model. A real loudspeaker has complex impedance, so Δ(dB) estimates the effect of series resistance on the response; it does not predict it. Rcable is computed as 2 · L · ρ / S, with ρ = 0.0175 Ω·mm²/m (copper at 20 °C); at 40 °C it rises to ≈0.0189 (with α ≈ 0.0039 /K). The "effective DF" includes the cable resistance on top of the amplifier's output impedance. In biwiring, two identical conductors following the same route in parallel reduce the equivalent resistance to half (L · ρ / S instead of 2 · L · ρ / S). In a real installation, the branches feed different sections of the crossover: the case is not strictly that of two resistors in parallel, and the crossover topology determines the effective effect. The 0.1 dB value corresponds to Lesurf's model (0.1 Ω cable, 8 Ω loudspeaker) and quantifies only the variation attributable to reducing the cable resistance, not the total effect of the series resistance on the response. The report does not adopt a universal audible advantage (Annex D.11). Developed in Part III.2.2 of the report.
6 · Q_res ↔ bandwidth ↔ octaves ↔ τ_res
Given a second-order resonator with centre frequency fc and quality factor Q_res, computes the −3 dB bandwidth, its equivalent in octaves, the number of cycles to −60 dB and the resonator decay time. It is the bridge between the REW waterfall, the time window and the resonances visible in the response.
CALCULATED Second-order resonator model (BANDPASS), impulse excitation, no added losses. τ_res is the resonator's decay time to −60 dB, NOT room T60 nor the 1/e time constant. Formulas: BW = fc/Q_res; BW_oct = log₂((√(1+1/(4Q²)) + 1/(2Q))/(√(1+1/(4Q²)) − 1/(2Q))); cycles(−60 dB) ≈ 2.2·Q_res; τ_res = cycles/fc. Valid for approximately minimum-phase modal peaks; not for cancellation nulls. Developed in Annex B and Annex D.5 of the report.
Section III · Interaction and measurement (3)
Delay, phase and source summation; critical distance and absorption; time window and frequency resolution. The interaction between loudspeaker and room, and the limits of measurement.
7 · Delay, phase and source summation
Two calculations that share the idea of signal combination. Delay ↔ phase ↔ polarity: given a path difference Δd (or a delay Δt), computes the phase shift at a crossover frequency f and the frequency at which the signal arrives inverted. Source summation: two sources with levels L1 and L2 sum differently depending on their coherence. They are ideal geometric phase shifts: they do not model filter phase, port group delay, EQ or the loudspeaker's response.
Delay ↔ phase ↔ polarity
Useful for aligning a subwoofer with the monitors, checking a reflection in the REW ETC or preparing a multisub.
CALCULATED Pure delay, no filter phase. c = 343 m/s. In a real system, the LR crossover, port group delay, EQ and the loudspeaker's own response add phase. f_inversion = c/(2·Δd) is the frequency at which the path difference equals half a wavelength; f_reinforcement = c/Δd is the frequency at which it equals a full wavelength. These are first-order bounds. For SBIR, the path difference is 2·d_wall (out and back): the null is at c/(4·d_wall), which is f_inversion with Δd = 2·d_wall. Final verification with the REW ETC and summation at the listening position is essential. Developed in Part III.1.2 of the report and Part IV.3.
Source summation (coherent vs incoherent)
In phase, coherent summation gives up to +6 dB; if incoherent, power summation gives +3 dB. With a phase shift Δφ, the vector sum falls between the two. The phase shift can be derived from the path difference Δd and the frequency f, or entered manually; the "Phase shift source" selector determines which field is the master and which is derived. This tool demonstrates visually why more drivers do not automatically equal more level: phase matters.
CALCULATED Summation at a single frequency. c = 343 m/s. Δφ is the phase difference at that f. Coherent = sources in phase (+6 dB if L1 = L2); incoherent = power summation (+3 dB if L1 = L2); vectorial = complex sum with cos(Δφ). With Δφ = 180° and L1 = L2, cancellation is total: the result is shown as "−∞ (total cancellation)". This is not the full-band response: for that, measure with REW and analyse the impulse response, or perform the vector sum frequency by frequency. Developed in Part I.4 of the report and Part II.2.
8 · Critical distance and absorption (Dc + Sabine)
Two tools for reasoning about the room without asking for materials. Dc (critical distance) is the point at which the direct and reverberant field levels are equal under the model's assumptions. It is not an abrupt physical boundary: below Dc the direct field dominates and above Dc the reverberant field does, but the result depends on directivity and on the room's conditions. Sabine what-if answers the question "how much absorption do I need to bring RT60 from X down to Y".
Dc — critical distance and direct vs reverberant level
Dc = 0.057 · √(Q_dir · V / RT60). Q_dir is the directivity factor: Q=1 omnidirectional, Q=2 half-space, Q=4 quarter-space. For an omnidirectional source, Q_dir = 1.
ΔL(r) = 20·log₁₀(Dc/r). At r = Dc, direct and reverberant are equal (0 dB). Below Dc the direct field dominates; above Dc the reverberant field does. It is an approximation: it does not replace a complete SPL prediction (which depends on radiated power and real directivity).
Sabine what-if — total absorption ↔ RT60
Sabine: RT60 = 0.161 · V / A, with A in m² Sabine. If you want to know how much absorption you need to reach a target RT60, enter V and the target RT60. Equivalent absorption does not translate automatically into a quantity of physical material: that requires frequency-dependent absorption coefficients, surface areas and mounting conditions.
CALCULATED Dc and Sabine: diffuse-field models. Valid above the Schroeder frequency; below it, modal distribution dominates and the concept of reverberant field loses meaning. A = Σ Si·αi (sum of surfaces by absorption coefficient). For the breakdown by materials, see the table in Annex B of the report. A high RT60 does not by itself prove that the sound will be subjectively "muddy": the decay of each mode should also be examined. Developed in Part III.1.1 and Annex C.
9 · Time window → frequency resolution
For a rectangular window, the frequency resolution of an FFT analysis is approximately Δf = 1 / T, with T in seconds and Δf in hertz. With T in milliseconds: Δf(Hz) = 1000 / T(ms). It is the inverse relationship between time window duration and frequency resolution. Two synchronised inputs.
Quick reference table
| Window | Δf rectangular | What you see in REW |
|---|---|---|
| 3 ms | 333 Hz | Mid-high, coarse resolution |
| 5 ms | 200 Hz | Report protocol IV.1 |
| 20 ms | 50 Hz | Lower modal region |
| 1000 ms (1 s) | 1 Hz | Narrow-band modal analysis |
CALCULATED Δf = 1 / T is the Rayleigh limit for a rectangular window (a separation criterion based on the first zero of the main lobe; it does not guarantee that two components will visually resolve in any analysis). REW applies the window chosen by the user; with Hann or Blackman-Harris the effective equivalent bandwidth is 1.5–2× larger than the rectangular value, so practical resolution is lower than the calculated value. It is not a universal property: the real factor depends on the specific window and on the resolution definition (main-lobe width, equivalent noise bandwidth, ability to resolve two tones). The number is the best theoretical case, not the exact resolution you will see in the graph. Developed in Part IV.1 of the report and Annex C.
Reference and auxiliaries
Elementary conversions (ms ↔ m, λ ↔ f ↔ T) and target curve slope illustration. Auxiliary operations that support the rest of the tools and refer back to the report's formulas.
A · Target curve slope — illustration
What a slope means in a frequency response graph. The grey curve is the flat reference (0 dB/octave); the cyan curve is the one you control with the slider; the amber dashed line is the mid-treble tendency of the Harman preference curve (−0.8 dB/octave). It is not a prescriptive target curve: the real Harman curve also includes a bass shelf (typically +4 to +10 dB below ~100–150 Hz) that this straight line does not represent. The report develops the argument in I.2 and III.1.3.
Move the slider or use an example to see what a slope means. All pivot at 1 kHz = 0 dB.
CALCULATED Calculation under declared assumptions: constant slope in dB/octave, anchored at 1 kHz = 0 dB, without modelling the room, the loudspeaker or the listener. The Harman reference line uses a slope of −0.8 dB/octave, cited in the literature as a mid-treble tendency; it does not include the bass shelf of the full curve and is not presented as a universal slope. The chart legend shows a linear slope on a logarithmic scale, anchored at 1 kHz, not a recommended equalisation target. The report does not fix a universal numerical slope (III.1.3). For the full argument on why "flat in room" is not the goal, see the blue callout of I.2.
B · Time ↔ distance converter (REW)
Direct conversion d = t · c / 1000 and t = d · 1000 / c, with c ≈ 343 m/s. Useful for translating an ETC peak in REW into path difference (outbound + return of the extra path). Path difference is a general geometric value. The distance to a specific wall is a later interpretation that depends on which reflection it is: only for a rear-wall reflection with normal incidence does dwall = t · c / 2000 hold. With a side wall, the geometry is different and the d/2 relationship does not apply.
c ≈ 343 m/s · Path difference: d = t · c / 1000 · Distance to rear wall with normal incidence: dwall = t · c / 2000
CALCULATED The conversion between time and path difference is general. The distance to the wall is a geometric interpretation that is only valid for a rear-wall reflection with normal incidence. With other geometry (side wall, ceiling, floor, object), the relationship between path difference and distance to the reflective surface is different. Developed in Annex C of the report.
C · Wavelength ↔ frequency ↔ period converter
λ = c / f · T = 1 / f. Three synchronised inputs. c selectable (15 / 20 / 25 °C) or custom. Useful for III.1.2 (SBIR), II.3 (the 82 Hz note), I.4 (centre spacing) and III.1.3 (panel absorption).
Frequency ↔ musical note table
| Note | Hz | λ (c = 343 m/s) |
|---|---|---|
| A0 | 27.5 | 12.47 m |
| E1 (bass) | 41.2 | 8.33 m |
| E2 (guitar) | 82.4 | 4.16 m |
| A2 | 110.0 | 3.12 m |
| C4 | 261.6 | 1.31 m |
CALCULATED Model in air at the selected c. 343 m/s is used by default, consistent with the report's example and with tools 1, 2, 7 and 8. The more precise value at 20 °C is 343.2 m/s, but the difference (0.06 %) does not change any conclusion. Note frequencies are approximations with equal temperament (A4 = 440 Hz). Developed in Annex B and Part III.1.2 of the report.
WHAT THIS PAGE CANNOT DO
What this page cannot do
Explicit, so no one mistakes a tool for a consultant:
- It does not recommend positions. Neither loudspeakers nor listener. Position depends on variables the dimensions do not contain.
- It does not say whether your room is "problematic". There is no universal threshold. The assessment depends on the measured response, the decay and the musical programme.
- It does not replace measuring. The fields on this page do not replace an impulse response and an averaged sweep.
- It does not calculate EPDR, complex impedance or PIR. They require curves, not scalars. PIR and EPDR are discussed in the report as diagrams and measurements, not as calculators.
- It does not estimate thermal compression. It requires multi-level measurements. In the report it is ND.
- It does not apply modal density indices. They are heuristic, not normative, and not actionable on an already-built room. The report does not use them.
- It does not ask about price. That logic is Mistake no. 5 in the report.
- It does not fix a target curve slope. The reference and auxiliaries section (target curve slope) illustrates what a slope means and shows the mid-treble tendency of the Harman reference; the preferred shape depends on the room, the listener and the programme.
- It does not calculate all room modes. The explorer shows the first axial modes, not the full set of eigenmodes (tangential and oblique).
This page is intended for domestic audio: one loudspeaker, one room, one listening position. If you need to estimate the SPL of a PA system with multiple cabinets, calculate ceiling loudspeaker coverage, arrays (end-fire, broadside), transition distance, DMX or lighting conversions, this page is not the right tool. For those cases, see PAcalculate by Doctor ProAudio: a professional suite, very comprehensive, maintained and also available as a free mobile app for Android and iOS.
The division is clean: PAcalculate calculates; this page explains the limits of what it calculates. If your case is domestic and you want to understand what you are measuring and why, you are in the right place. If your case is professional and you only need the number, PAcalculate will give it to you faster and with more options.