How this calculator works
- Step 1Level10 log(I ÷ I₀)I₀ = 10⁻¹² W/m², the threshold of hearing.
- Step 2Sources+10 log NIntensities add, not decibels.
- Step 3Distance−20 log(r₂ ÷ r₁)Inverse-square spreading.
Decibels measure sound intensity on a logarithmic scale. Every 10 dB is ten times the intensity, so decibels from separate sources cannot simply be added.
In open air, sound from a small source spreads over a growing sphere. Its intensity falls with the square of distance: about 6 dB less for every doubling.
Worked example: 85 dB at 1 m, heard at 2 m
- L₂
L₁ − 20 log₁₀(r₂ ÷ r₁)
- Level at 1 m85 dB
- Distance change−20 log₁₀(2)−6.0 dB
- Level at 2 m79.0 dB
Read the result
Two 60 dB sources together make 63.0 dB. Ten 90 dB machines heard ten times as far away give 80.0 dB.
- Double the sources+3 dBTwice the intensity.
- Double the distance−6 dBA quarter of the intensity.
Assumptions and limits
- Point sourcesSmall compared with the distance.
- IncoherentSeparate sources, not one signal split.
- No wallsRooms and echoes keep levels higher.
- Not hearing adviceFor safe-exposure limits, follow occupational rules.
Related logarithm tools
Decibels are a logarithmic scale, so adding sources does not add their levels.
To see the logarithms behind each step, use the log calculator. For other waves, the wavelength and frequency calculator converts between the two.
Common mistakes
Mistake: Adding 60 dB + 60 dB = 120 dB.
Instead: Two equal sources give about 63 dB.
Mistake: Expecting −6 dB per doubling indoors.
Instead: Reflections make the drop smaller.
Checking the method
A separate script converts every level to watts per square metre, adds and scales the intensities, and only then converts back to decibels.
Read how we test our calculators, or browse more maths calculators.