Skip to content
Conversionsscience

Sound Level (Decibel) Calculator

Combining sound levels and the effect of distance. Decibels are logarithmic, so two identical sources add three decibels rather than doubling, and ten decibels is roughly a doubling of perceived loudness.

Also called: sound level calculator, db addition.

dB
dB
Combined level
88.01

Two sources at 85 and 85 dB combine to 88.01 dB, not their sum. 88.01 dB for 2 identical sources. Moving 2 times further away drops it by 6.02 dB. Decibels are logarithmic, so they add by intensity rather than arithmetically. Two equal sources add three decibels.

Level from n identical sources
88.01
Drop from distance
6.02
Level at the new distance
78.98
Intensity ratio between the two levels
1
Perceived loudness ratio
1
On the logarithmic scale
Decibels are logarithmic, so they add by intensity rather than arithmetically. Two equal sources add three decibels.
How this is calculated
Method and background

How this is calculated

Decibels measure a ratio on a logarithmic scale, so they cannot be added directly. Combining sources means converting to intensity, adding, and converting back, which gives three decibels for two equal sources and ten for ten of them. Distance follows the inverse square law: doubling the distance drops the level by six decibels in free field. Perception is different again, with roughly ten decibels needed for a sound to seem twice as loud, which is why a three decibel increase is measurable and barely noticeable.

levels combine by adding intensities, not decibels, so two equal sources add three decibels
L
Sound level

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

two equal sources

First level
85 dB
Second level, to combine
85 dB
Or, number of identical sources
2
Distance multiplied by
2

Combined level88.01

10 log10(2) is 3.01; 20 log10(2) is 6.02

Open this example

ten sources add ten decibels

First level
85 dB
Second level, to combine
85 dB
Or, number of identical sources
10
Distance multiplied by
1

Combined level88.01

boundary: the definitional case for a factor of ten

Open this example

Method and limits

What it assumes

  • Incoherent sources in a free field, with no reflections.

What it deliberately does not model

  • Indoors, reflections mean the inverse square law understates the level at distance.
  • Perceived loudness depends on frequency, which A-weighting only partly captures.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Why do two 85 dB sources make 88 and not 170?
Because decibels are logarithmic. Doubling the intensity adds ten times the log of two, which is about three decibels.
How much louder is 10 dB?
Ten times the intensity, but only about twice as loud to a listener. Perception and intensity are different scales.