Decibels Calculator

Decibels compress an enormous range of sound pressures into a manageable scale. The formula is logarithmic, which is why adding three decibels roughly doubles the intensity.

Sound pressurePascals, as a root mean square value. 0.2 is roughly a busy street.Reference pressurePascals. Twenty micropascals is the standard reference for sound in air.

Sound pressure level

Pressure ratio to the reference: 10,000
Intensity ratio: 100,000,000
Decibels added by doubling: 6.0206

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

dB = 20 x log(pressure / reference pressure)

dB: Sound pressure level in decibels
p: Measured sound pressure, in pascals
p0: Reference pressure, 20 micropascals for sound in air
ratio: Measured pressure divided by the reference pressure

How to check the result by hand

1
Measure the sound pressure
In pascals, and as a root mean square value rather than a peak. The default of 0.2 pascals is roughly the pressure of a busy street.
2
Divide by the reference pressure
The reference for sound in air is 0.00002 pascals. Point two divided by that is ten thousand, a pure ratio with no units.
3
Take the base ten logarithm
The logarithm of ten thousand is four, because ten to the power four is ten thousand. This is the step that compresses the enormous range.
4
Multiply by twenty
Four times twenty is eighty decibels. The factor is twenty for pressure because intensity is proportional to pressure squared.
5
Compare with familiar levels
Eighty decibels is a busy street or a vacuum cleaner. Normal conversation sits near sixty and anything sustained above eighty five risks hearing damage.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Decibels page.