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Decibel Addition Calculator

Combine two decibel levels into one.

How it is calculated

Decibels are logarithmic, so levels from different sources must be added as sound energy, not as plain numbers. The tool converts each level to a relative power, adds them and converts back: L = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10)), with L₁ and L₂ in dB. The result is rounded to two decimals.

The formula is for sources that are independent (uncorrelated) and measured at the same point, and both levels need to use the same reference and weighting, such as dB(A). It handles two levels at a time; for three sources add two, then add the third to that total. Zero and negative levels are accepted because dB is relative.

Worked example

Two machines each produce 70 dB at the listener's position. Each is 10^(70/10) = 10^7 = 10,000,000 in relative power. The sum is 20,000,000. L = 10 × log₁₀(20,000,000) = 10 × 7.301 = 73.01 dB. Doubling the sources adds only about 3 dB, not 70.

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Common mistakes

  • Adding decibels arithmetically (70 + 70 = 140). The correct figure for two equal sources is about 3 dB above one of them.
  • Expecting a quiet source to matter next to a loud one. Adding 60 dB to 80 dB gives about 80.04 dB, so the quieter source is almost lost.
  • Mixing weightings, such as dB(A) for one source and dB(C) for another, or levels measured at different distances.
  • Using the formula for sources with a fixed phase relationship, like two speakers playing the same tone, where waves can reinforce or cancel.

About this calculator

Because decibels are a logarithmic scale, two sound sources cannot simply be added arithmetically — a source at 70 dB next to another at 70 dB does not produce 140 dB. Instead, the combined level is L_total = 10·log₁₀(10^(L₁/10) + 10^(L₂/10)), which converts each level back to raw sound intensity, adds the intensities linearly, and converts the sum back to decibels. Two equal, incoherent sources combine to add about 3 dB to a single source's level, not double it.

Acoustic and noise-control engineers use this to predict the combined noise level of multiple machines, fans, or traffic lanes; audio engineers use it when summing microphone or speaker outputs; and occupational health and safety professionals use it to assess whether combined workplace noise exceeds exposure limits. Urban planners and environmental consultants also rely on it to model cumulative noise from combined sources like nearby roads or construction equipment.

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