# dB Calculator

Created by Krishna Nelaturu
Last updated: Feb 18, 2023

This dB calculator is here to help you express the sound pressure level (SPL) and sound intensity level (SIL) in decibels (dB). It essentially converts sound pressure and sound intensity to decibels. In this article, we shall consider some fundamental questions regarding decibel calculation, including:

• What are sound pressure level and intensity level?
• How to calculate SPL and SIL in dB?

If you need a refresher on sound waves, you'll love our sound wavelength calculator.

## What is sound pressure level? How to calculate SPL in decibels?

Sound pressure is the pressure caused by a sound wave moving through a medium. Like any other pressure, we measure it in Pascals. However, a more convenient method of measuring sound pressure is to compare it to a reference sound pressure on a logarithmic scale. We define sound pressure level (SPL) as the logarithmic measure of sound pressure relative to the human hearing threshold. The formula for sound pressure level is given by:

$L_p = 20 \log \left( \frac{p}{p_0}\right) \text{dB}$

where:

• $L_p$ - The sound pressure level in decibels (dB);
• $p$ - The sound pressure of interest in pascals; and
• $p_0$ - The reference sound pressure. It is common to use the human hearing threshold in air, equal to $p_0 = 20 \mu\text{Pa} = 0.00002\text{ Pa}$.

Generally, we can use the notations $L_p$ and $\text{dB(SPL)}$ interchangeably.

The medium of sound propagation is important too. For example, the reference sound pressure for water is $p_0 = 1\mu\text{Pa}$. Learn more about a medium's effect on sound speed through our speed of sound calculator.

## What is sound intensity level? How to calculate it in decibels?

Sound intensity is the power a sound wave carries per unit area perpendicular to the direction of sound propagation. The SI units are $\text{W/m}^2$. Like SPL, we can conveniently express the good intensity on a logarithmic scale. We define the sound intensity level (SIL) as the logarithmic measure of sound intensity relative to a reference intensity value. The formula for sound intensity level is given by:

$L_I = 10\log \left(\frac{I}{I_0} \right) \text{dB}$

where:

• $L_I$ - The sound intensity level;
• $I$ - The sound intensity of interest in $\text{W/m}^2$; and
• $I_0$ - The reference sound intensity. For air, it is common to use $I_0 = 1 \text{ pW/m}^2$.

## How to use this dB calculator?

We trust that you now understand how this dB calculator achieves the dB conversion of sound pressure and sound intensity to decibels.

To calculate SPL from the sound pressure, use the sound pressure level section:

1. Enter the reference pressure value. We set it to $0.00002\text{ Pa}$ for air, but you can change this value for another medium.
2. Enter the sound pressure value. This dB calculator will automatically calculate SPL in dB.

To calculate SIL from the sound intensity, use the sound intensity level section:

1. Enter the reference sound intensity value. We set it to $0.000000000001\text{ W/m}^2$ for air, but you can change this value for another medium.
2. Enter the sound intensity value. This decibel calculator will automatically calculate SPL in dB.

Since this decibel calculator is versatile, you can use it in reverse for dB conversion to convert dB to Pa or dB to W/m2. Try converting 50 dB to Pa and W/m2.

Krishna Nelaturu
Sound pressure level
Ref. pressure
psi
Pressure
psi
SPL
dB
Sound intensity level
Ref. intensity
W
/m²
Intensity
W
/m²
SIL
dB
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