Acoustic Power Calculator Formula

Understand the math behind the acoustic power calculator. Each variable explained with a worked example.

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Formulas Used

Sound Power Level

power_level = 10 * log10(power / 1e-12)

Intensity at 1 m (free field)

intensity_1m = power / (4 * pi * 1)

Variables

VariableDescriptionDefault
powerSound Power(W)0.01

How It Works

Sound Power Level

Sound power is the total acoustic energy emitted by a source per second, independent of distance or room.

Formula

Lw = 10 log10(W / W0)

  • *W* = sound power (watts)
  • *W0* = 10^-12 W (reference)

    • Sound power is an intrinsic property of the source. Intensity at distance r in free field: I = W / (4 pi r^2).

    Worked Example

    A loudspeaker emitting 0.01 W.

    power = 0.01
    1. 01Lw = 10 log10(0.01 / 1e-12)
    2. 02Lw = 10 log10(1e10)
    3. 03Lw = 10 * 10 = 100 dB
    4. 04Intensity at 1 m = 0.01 / (4 pi) = 7.96e-4 W/m2

    Frequently Asked Questions

    How does sound power differ from sound pressure level?

    Power is the total energy output (property of the source). Pressure level depends on distance and the acoustic environment. Power is measured in watts; SPL in dB re 20 micropascals.

    How is sound power measured?

    In a reverberation room (comparing with a reference source) or an anechoic chamber (integrating intensity over a surface enclosing the source).

    What is a typical sound power for speech?

    Normal speech produces about 10 to 50 microwatts (about 70 to 77 dB Lw). Shouting can reach 1 milliwatt.

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