AC-02Acoustic Fundamentals

Decibel ⇄ Linear Converter

Convert between levels in dB and physical quantities: pressure, intensity, power, velocity, acceleration, voltage.

Inputs

Quantity

Level (re 20 µPa)

Linear value

Drag either slider - they are linked.

Level

94.00dB

Linear value

1.002Pa

Amplitude ratio

50,120×

Energy ratio

2.512e9×

Plane-wave intensity (ρc = 413)

0.00243W/m²

Same pressure underwater

120.0dB re 1 µPa

Transfer curve20 · log₁₀(x / 20 µPa)

Sound level ladderclosest: 94 dB

Threshold of hearing at 1 kHz

Breathing; anechoic chamber

Rustling leaves; recording studio

Whisper at 1 m; quiet bedroom

Library; quiet office

Refrigerator hum; light rain

Conversation at 1 m

Vacuum cleaner; busy street

Heavy traffic at kerb; EU lower action value

Food blender; hearing protection advised

Acoustic calibrator (1 Pa)◀ 94.0

100

Pneumatic drill at 2 m

110

Rock concert, front rows

120

Thunderclap; chainsaw at the ear

130

Threshold of pain

140

Jet engine at 30 m; peak exposure limit

160

Rifle shot at the shooter’s ear

194

1 atm peak - limit of undistorted sound in air

§ Theory of operation

Power quantities and field quantities

The bel is the base-10 logarithm of a ratio of two power quantities; the decibel is a tenth of it. Intensity and sound power are power quantities, so:

L = 10\,\log_{10}\!\left(W\,/\,W_0\right) \qquad \text{[power, intensity]}

Pressure, velocity, acceleration and voltage are field (root-power) quantities, power is proportional to their square, so the factor becomes 20:

L = 20\,\log_{10}\!\left(p\,/\,p_0\right) = 10\,\log_{10}\!\left(p^2\,/\,p_0^2\right)

Because of this, +6 dB doubles a pressure while +3 dB doubles a power. Both describe the same change in energy only when the quantity type is respected.

Reference values

Quantity	Reference	Standard
Sound pressure (air)	20 µPa	ISO 1683
Sound intensity	1 pW/m²	ISO 1683
Sound power	1 pW	ISO 1683
Vibration velocity	1 nm/s	ISO 1683
Vibration acceleration	1 µm/s²	ISO 1683
Voltage (dBV)	1 V	- (dBu uses 0.775 V)

Always quote the reference: “80 dB” is meaningless for vibration unless you know whether it is re 1 nm/s, re 10 nm/s (older practice), or re 1 µm/s². In water acoustics, sound pressure is referenced to 1 µPa, giving numbers 26 dB higher than in air for the same pressure.

Useful ratios

ΔL	Field ratio	Power ratio
1 dB	×1.122	×1.259
3 dB	×1.413	×2.0
6 dB	×2.0	×3.98
10 dB	×3.16	×10
20 dB	×10	×100