dB Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Mar 08, 2022

This dB calculator will help you find the sound pressure level (SPL) and intensity level in decibels. You can use it for dB conversion or for determining the distance from the source of a sound.

Make sure to try our wavelength calculator if you want to know the frequency of the sound waves, and the speed of sound calculator for their exact speed in a given medium.

Sound pressure level (SPL)

When we hear a very loud noise, we experience unpleasant feelings. It is because of the pressure of a sound wave. Even though this pressure can be measured in Pascals, like air pressure, it is more practical to use decibels - a logarithmic unit. The sound pressure level, or SPL, is simply the measure of sound pressure with reference to the human hearing threshold.

SPL = 20log(P/Pref)

where:

  • SPL is the sound pressure level in dB;
  • P is the sound wave pressure, measured in pascals; and
  • Pref is the reference value of sound pressure. Typically, it is assumed to be equal to 0.00002 Pa.

As you probably noticed, the SPL increases logarithmically. Also, it is a relative measure, while the regular sound wave pressure is an absolute measure of loudness.

Sound intensity level (SIL)

Sound intensity is defined as the sound wave power per unit area. It is a special quantity that allows us to measure the energy of sound (or, to be more precise, the energy per second per one squared meter).

SIL = 10log(I/Iref)

where:

  • SIL is the sound intensity level in dB;
  • I is the sound intensity in watts per squared meter;
  • Iref is the reference value if sound intensity. Typically, it is assumed to be equal to 1×10⁻¹² W/m².
Table of examples of sound pressures and intensity values
Examples of sounds with corresponding values of sound pressure in decibels and Pascals, and sound intensity.
Source: Evergreen State College / CC-BY-SA

Sound intensity at a distance

Sound intensity changes with the distance from the sound source. It's just common sense - if a car passes you, you hear a loud noise that gets quieter as the car moves away. This phenomenon is also known as distance attenuation.

From a physical point of view, it happens because the energy of sound is now distributed over a larger area. Imagine a sphere surrounding the sound source. Even though the energy emitted by the source is constant, the sphere can get larger - its surface will increase. The energy will be distributed over the area of the sphere. Not surprisingly, we can write it down in the form of an equation as:

I = P/(4πR²)

where R is the radius of the sphere - the distance from the sound source.

The attenuation of power radiated by a source with an increase in distance is a characteristic of all electromagnetic radiations.

For different materials, the intensity of the sound is also affected. The medium’s property that describes how the sound wave’s intensity is affected is known as acoustic impedance (Z).

Pascals to dB conversion

Our decibel calculator can be used for finding the equivalent of sound wave pressure in decibels. Simply type the pressure in pascals into the dB calculator to find the sound pressure level. You can also use this tool in reverse to find the pressure if SPL is given.

If you're interested in acoustics, make sure to take a look at the reverberation time calculator, too!

Bogna Szyk
Sound pressure level
Ref. pressure
psi
Pressure
psi
SPL
dB
Sound intensity level
Ref. intensity
W
/m²
Intensity
W
/m²
SIL
dB
Distance
m
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