Decibel Calculator
Combine multiple sound sources, convert between decibels and ratios, and work out how loudness falls with distance.
How to use this calculator
- 1To combine sources, enter each level in decibels separated by commas.
- 2To find the level at a different distance, enter the known level and both distances.
- 3To convert a ratio, choose whether it is a power or an amplitude quantity — the multiplier differs.
How the calculation works
power: dB = 10 log₁₀(P₁/P₀) amplitude: dB = 20 log₁₀(A₁/A₀) combining: L = 10 log₁₀(Σ 10^(Lᵢ/10)) distance: ΔL = −20 log₁₀(d₂/d₁)- dB
- Decibel — a tenth of a bel, a logarithmic ratio between two quantities
- 10 log
- Used for power, intensity and energy ratios
- 20 log
- Used for amplitude, voltage and pressure — quantities whose square gives power
- Lᵢ
- The level of each individual source when combining several
Decibels never add arithmetically. Two 85 dB sources give 88 dB, not 170. Each level must be converted back to a power ratio, summed, and converted again.
Two equal sources always add exactly 3.01 dB, because that is 10 log₁₀(2). Ten equal sources add exactly 10 dB. These are the two figures worth memorising.
A point source loses 6.02 dB per doubling of distance, which is the inverse square law expressed logarithmically. A line source such as a road loses only 3 dB, because the sound spreads cylindrically rather than spherically.
Sound pressure level is referenced to 20 micropascals, the approximate threshold of human hearing at 1 kHz. That is what makes 0 dB SPL "silence" rather than the absence of sound.
Worked example
Two 85 dB machines running together
- 1.Convert each to a power ratio: 10^(85/10) = 10^8.5 = 3.162 × 10⁸ each.
- 2.Sum them: 6.324 × 10⁸.
- 3.Convert back: 10 × log₁₀(6.324 × 10⁸) = 88.01 dB.
- 4.Two equal sources add exactly 3.01 dB — never 170 dB, and never 6 dB.
- 5.To get a meaningful reduction you must remove one entirely, which gains only 3 dB back.
Result: 88.01 dB
A 90 dB source heard from 10 metres
- 1.The level is 90 dB at 1 metre.
- 2.The distance ratio is 10 ÷ 1 = 10.
- 3.Change: −20 × log₁₀(10) = −20 dB.
- 4.Level at 10 m: 90 − 20 = 70 dB.
- 5.Each doubling costs 6.02 dB: 1→2 m loses 6, 2→4 loses another 6, and so on.
Result: 70 dB at 10 metres
Why 85 dB plus 85 dB is 88 dB
Decibels are logarithms, and logarithms do not add when the underlying quantities do. Adding two sound levels means adding the acoustic powers they represent, then converting the total back to decibels — and doubling a power is 10 log₁₀(2) = 3.01 dB.
So two identical machines produce 3 dB more than one. Four produce 6 dB more. Ten produce 10 dB more. The pattern is worth internalising because it governs every practical noise decision: silencing one of two identical machines buys back only 3 dB, which is barely perceptible.
The reverse consequence is more useful. When sources differ, the loudest dominates almost completely. A source 10 dB below another contributes just 0.41 dB to the total; one 20 dB below contributes 0.04 dB. Noise control means finding the single loudest source and dealing with it, because nothing else moves the number.
The 10 log / 20 log distinction
Decibels use 10 log for power quantities and 20 log for amplitude quantities, and mixing them up is the most common error in the field. It is not an inconsistency in the definition — it is what keeps the definition consistent.
Power is proportional to amplitude squared. Since log(x²) = 2 log(x), expressing a change in amplitude terms needs twice the multiplier to describe the same physical change. Double the voltage and you quadruple the power; both are correctly reported as 6.02 dB, one via 20 log₁₀(2) and the other via 10 log₁₀(4).
In acoustics, sound pressure is an amplitude quantity and uses 20 log, while sound intensity is a power quantity and uses 10 log. Sound pressure level is what a meter reads and what "dB SPL" refers to, referenced to 20 micropascals — roughly the quietest sound a healthy young ear can detect at 1 kHz.
What this assumes, and where it stops
Assumptions
- Sources are uncorrelated, so their powers add. Correlated sources can interfere and add differently.
- The distance calculation assumes a point source radiating freely into open space with no reflections.
- Levels are unweighted. A-weighted measurements (dBA) apply a frequency correction not modelled here.
Limitations
- Free-field only. Indoors, reflections stop the level falling with distance as calculated, and beyond the critical distance it barely falls at all.
- Point sources only. A line source such as a motorway loses about 3 dB per doubling of distance rather than 6.
- Ignores air absorption, which becomes significant at high frequencies over long distances, and ground and barrier effects.
- Does not convert between weightings, or model how loud something actually sounds — perceived loudness follows roughly a 10 dB doubling, not the 3 dB that doubles the power.
Common questions
How do you add decibels?
Not arithmetically. Convert each level to a power ratio with 10^(L/10), add those, then convert back with 10 log₁₀ of the total. Two 85 dB sources give 88.01 dB, not 170. Two equal sources always add exactly 3.01 dB.
How much quieter is a sound twice as far away?
6.02 dB quieter, for a point source in open air. Sound spreads over a sphere whose area grows with the square of distance, so intensity falls fourfold per doubling — which is 6 dB. A line source like a road loses only about 3 dB per doubling.
When do I use 10 log versus 20 log?
Use 10 log for power, intensity and energy; 20 log for amplitude, voltage and sound pressure. Power scales with amplitude squared, and the factor of 2 in the multiplier compensates exactly, so both describe the same physical change with the same decibel figure.
Does 3 dB sound twice as loud?
No. 3 dB is double the acoustic power, but perceived loudness roughly doubles only around a 10 dB increase. A 3 dB change is close to the smallest difference most people notice at all, which is why halving the number of noise sources sounds so disappointing.
Sources
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
Related calculators
Tools people commonly use alongside the decibel calculator.