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Sound Engineering
Calculators

Twelve working calculators for the numbers that decide whether a room holds: impedance loads, amplifier matching, level conversion, SPL, delay alignment, cable loss, room modes, and reverberation. Every formula checked against the standards.

Speaker Impedance Loads

Add speakers, choose wiring, and see the total load the amplifier sees plus how power divides among the speakers.

Add speaker
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Parallel: 1/Z = 1/Z₁ + 1/Z₂ + …  |  Series: Z = Z₁ + Z₂ + …
Add at least one speaker to begin.

Amp ↔ Speaker Matching

Recommended amplifier size from the speaker’s continuous (AES/RMS) rating. Rule of thumb: amp ≈ 1.5–2× continuous rating at the speaker’s impedance.

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Amp range = 1.5× to 2× P_continuous  |  Headroom target = P_cont × 10^(headroom/10)
Underpowering: an amp much smaller than the rating that gets pushed into clipping sends distorted (high average) power that cooks drivers , clipping kills more speakers than clean power. Overpowering: above ~2× continuous you risk mechanical/thermal damage on sustained peaks; use limiters and mix discipline.

Level Converter: dBu ↔ dBV ↔ Volts

Edit any field; the others update. 0 dBu = 0.7746 V, 0 dBV = 1.000 V.

dBu = 20·log₁₀(V / 0.7746)  |  dBV = 20·log₁₀(V / 1.000)  |  dBu = dBV + 2.218

Ratio → dB

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dB = 10·log₁₀(P₂/P₁)  |  dB = 20·log₁₀(V₂/V₁)

SPL Addition (Incoherent Sources)

Combined level of up to 4 uncorrelated sources (different signals, e.g. band + crowd + HVAC). Leave unused fields blank.

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L_total = 10·log₁₀( Σ 10^(Lᵢ/10) )

SPL at Distance

Predicted SPL from speaker sensitivity, applied power, and listener distance (free field).

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SPL = Sens + 10·log₁₀(P) − 20·log₁₀(d)

Level Change Between Two Distances

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ΔSPL = 20·log₁₀(d₁/d₂)  (point source; uses 10·log₁₀ when line-source toggle is on above)

Distance → Delay Time

Time for sound to travel a distance, temperature-corrected. Use for delay-tower and fill alignment.

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c = 331.3 + 0.606·T (m/s)  |  t = d / c × 1000 (ms)

Delay Time → Distance

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d = t/1000 × c  where  c = 331.3 + 0.606·T
Haas / precedence zone quick reference: arrivals within ~1–30 ms of the first sound fuse into one image localized to the earlier arrival. Typical practice: delay fills to main arrival + 5–15 ms “behind” to keep the image at the stage. Beyond ~35–40 ms, the later arrival is heard as a discrete echo.

Speaker Cable & Voltage Drop

Losses in a passive speaker run. Cable resistance uses both conductors (round trip = 2 × length).

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R_cable = 2·L·R/m  |  drop% = R_c/(R_c+Z)×100  |  loss dB = 20·log₁₀((Z+R_c)/Z)  |  DF_max = Z/R_c

Axial Room Modes

First 10 axial (single-dimension) standing-wave frequencies per dimension. Speed of sound assumed 343 m/s (20 °C).

f = n·c / (2·dimension), n = 1…10, c = 343 m/s  |  f_Schroeder = 2000·√(RT60/V)
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Frequencies marked in orange are within 5% of a mode from another dimension , stacked (near-coincident) modes reinforce each other and are the strongest candidates for bass trapping or subwoofer/listener repositioning. Below the Schroeder frequency the room behaves modally; above it, statistically (reverberant).

RT60 , Sabine Reverberation Time

RT60 = 0.161 · V / A (metric: V in m³, A in metric sabins = Σ surface area × absorption coefficient).

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RT60 = 0.161 · V / A  (metric)  |  RT60 = 0.049 · V / A  (imperial)
Validity: Sabine assumes a diffuse field and low mean absorption (α ≲ 0.2). In heavily treated or very absorptive rooms it over-predicts RT60 , use Norris–Eyring instead. It also ignores air absorption, which matters above ~2 kHz in large volumes.
UseTypical RT60 target
Speech / teaching0.6 – 1.0 s
Contemporary worship / amplified music1.0 – 1.5 s
Classical / choral / organ1.8 – 2.2 s

On these numbers. These are standard live-sound and acoustics formulas (free-field propagation, ideal constant-voltage amplifier, solid-copper conductors at 20 °C, Sabine statistical assumptions, axial room modes only). They are accurate for design and estimation , they are not a substitute for measurement. Verify critical systems in the room, under load, with instruments.

The numbers are the easy part.

Getting a room to actually hold on a Sunday, a graduation, or a live broadcast takes more than a calculator. If you want the system measured, tuned, and documented so it survives the person who built it , that is the work we do.

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