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Decibel Addition Calculator

Work out decibel addition instantly with clear inputs, formula shown and shareable results.

About Decibel Addition Calculator

Decibels cannot be added arithmetically - the intensities add, so each level must be converted back to a power ratio first. 85 dB and 82 dB combine to 86.8 dB, not 167 dB. Two identical sources always give exactly 3 dB more, and a source 10 dB quieter adds only 0.4 dB.

Formulas

Logarithmic addition

L = 10 log10(10^(L1/10) + 10^(L2/10))

Equal sources

two equal levels add 3.01 dB

Worked example

With the default values below, Decibel Addition Calculator returns Combined Sound Level of 86.76. Change any input above and every figure here is recalculated in your browser.

Inputs used

First sound level
85 dB
Second sound level
82 dB

Results

Combined Sound Level
86.76 dB
Increase Over The Louder Source
1.764 dB
Gap Between The Two Sources
3.00 dB
What Simple Addition Would Wrongly Give
167.0 dB

Step by step

  1. 1Values used
  2. 2Logarithmic addition
  3. 3Equal sources
  4. 4Combined Sound Level= 86.76 dB
  5. 5Increase Over The Louder Source= 1.764 dB
  6. 6Gap Between The Two Sources= 3.00 dB
  7. 7What Simple Addition Would Wrongly Give= 167.0 dB

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do two identical machines give only 3 dB more?

Because the intensity doubles, and 10 log10(2) is 3.01 dB. Doubling power is a 3 dB step, not a doubling of the number.

When can I ignore the quieter source?

Once it is more than 10 dB below, it contributes under 0.5 dB - usually inside measurement uncertainty.

Related Calculators

Decibel Addition Calculator – Calculate Combined Sound Level