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Math & Numbers

Sound Power Level Converter (W / dB Lw re 1 pW)

· Last updated：2026-08-01

Convert sound power between linear units (W, mW, µW, pW) and the decibel sound power level dB Lw (Lw = 10·log₁₀(W / 1 pW), reference P₀ = 1 pW = 1e-12 W, per ISO 3744 / IEC 60027-3). Supports bidirectional linear↔logarithmic conversion and reports the equivalent value in all five units. Reference values: whisper ≈ 1e-9 W (Lw ≈ 30), speech ≈ 1e-5 W (Lw ≈ 70), jet engine at 1 m ≈ 1e4 W (Lw ≈ 160).

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Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
select, number
Output type
json
Sample coverage
4
API ready
Yes

Overview

Convert sound power between W, mW, µW, pW, and dB Lw relative to 1 pW. Enter a value in any supported unit to calculate the equivalent sound power, with results reported across all five units.

When to use

  • Convert a measured or calculated sound power value from watts to dB Lw.
  • Convert a dB Lw value back to linear power units such as W, µW, or pW.
  • Compare acoustic power values using a consistent reference of 1 pW.

How it works

  1. 1Select the input unit: W, mW, µW, pW, or dB Lw.
  2. 2Enter a non-negative linear power value or a finite dB Lw value.
  3. 3Choose the preferred output unit and set the number of decimal places from 0 to 10.
  4. 4The converter applies Lw = 10·log₁₀(W / 1 pW) or the inverse calculation and reports equivalent values in all five units.

Use cases

  • Acoustic engineering calculations that require sound power and sound power level conversions.
  • Noise emission documentation using dB Lw with the 1 pW reference.
  • Educational and technical comparisons of values such as whisper-level and speech-level sound power.

Examples

1. Convert speech sound power to dB Lw

Acoustic engineer

Background

An acoustic engineer has a speech sound power estimate of 1e-5 W and needs its corresponding sound power level.

Problem

Convert the linear value into dB Lw relative to 1 pW.

How to use

Select W as the input unit, enter 0.00001, select dB Lw as the output unit, and use 6 decimal places.

{"inputUnit":"W","value":0.00001,"outputUnit":"dB Lw","decimalPlaces":6}

Outcome

The result is 70 dB Lw. The equivalent values are 0.00001 W, 0.01 mW, 10 µW, and 10000000 pW.

2. Convert a whisper-level value to microwatts

Audio technician

Background

An audio technician is working with a whisper-level sound power value expressed as 30 dB Lw.

Problem

Convert the logarithmic level into a linear value in µW.

How to use

Select dB Lw as the input unit, enter 30, select µW as the output unit, and use 6 decimal places.

FAQ

What reference does dB Lw use?

dB Lw uses a reference sound power of 1 pW, equal to 1e-12 W.

Can I convert dB Lw to watts?

Yes. Select dB Lw as the input unit and W as the output unit.

Which input units are supported?

The converter accepts W, mW, µW, pW, and dB Lw.

What values are valid for linear power?

Linear sound power must be non-negative. dB Lw values must be finite.

How is the result rounded?

Set Decimal Places to a value from 0 to 10. The default is 6 decimal places.

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{"inputUnit":"dB Lw","value":30,"outputUnit":"µW","decimalPlaces":6}

Outcome

The result is 0.001 µW, equivalent to 1e-9 W, 0.000001 mW, 1000 pW, and 30 dB Lw.