Decibel addition calculator
Type two or more levels in dB. Decibels are logarithmic, so they cannot be added like ordinary numbers: the calculator turns them into energy, adds, and turns the sum back into dB. It can also remove background noise from a measurement and average levels.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Type the levels in dB, separated by commas, spaces or semicolons.
- Choose add to combine sources that play at once, subtract to take background or other sources out of a total, or energy average.
- Read the result, the difference from the loudest level (or from the total) and the plain arithmetic mean for comparison.
How it works
Every level is turned into a relative energy, 10^(L ÷ 10).
- Add: L = 10 × log₁₀ Σ 10^(Lᵢ ÷ 10)
- Subtract: L = 10 × log₁₀(10^(L₁ ÷ 10) − Σ 10^(Lᵢ ÷ 10)), where L₁ is the first level
- Energy average: L = 10 × log₁₀(Σ 10^(Lᵢ ÷ 10) ÷ n)
This holds for uncorrelated sources, such as different machines or instruments, which is nearly always the case for noise. It works for any dB scale (dB SPL, dBA, dBm) as long as all values are in the same one.
Worked example
Three machines at 85, 88 and 90 dB:
- energies: 10^8.5 = 316,227,766; 10^8.8 = 630,957,344; 10^9 = 1,000,000,000;
- sum 1,947,185,110; 10 × log₁₀ = 92.89 dB;
- that is 2.89 dB above the loudest machine alone, while the arithmetic mean would be 87.67 dB.
Tips
- A source 10 dB quieter than another adds only 0.4 dB to it: tackle the loudest noise first.
- Two equal sources always add 3.01 dB, whatever the level.
- To find how loud a speaker plays at a distance, use the speaker SPL calculator.
Frequently asked questions
What is 90 dB plus 90 dB?
93 dB, not 180 dB. Two equal sources double the sound energy, and doubling energy adds 10 × log₁₀ 2 ≈ 3 dB. Ten equal sources add 10 dB.
How do you add decibels?
Turn each level into relative energy with 10^(L ÷ 10), add the energies and take 10 × log₁₀ of the sum. For 85, 88 and 90 dB: 10^8.5 + 10^8.8 + 10^9 = 1.947 × 10⁹, and 10 × log₁₀ of that is 92.89 dB.
How do I remove background noise from a measurement?
Choose subtract and enter the total first, then the background. A machine measured at 95 dB with 90 dB of background on its own is 10 × log₁₀(10^9.5 − 10^9) = 93.35 dB. If the difference is under about 3 dB the result is very uncertain.
Why not just average the dB values?
An arithmetic mean of 80 and 90 dB is 85 dB, but the louder level carries ten times the energy. The energy average is 10 × log₁₀((10⁸ + 10⁹) ÷ 2) = 87.40 dB, which is how a sound level meter would average them.