Combining Decibels Calculator

Combining Decibels

Decibels are logarithmic — you cannot simply add them. Two equal-loudness sources do not give 2× the dB; they add only 3 dB. This is one of the most common acoustic mistakes in noise reports and live-sound mixing.

Formula

L_total = 10 × log₁₀(Σ 10^(L_i / 10))

Convert each dB level back to linear power, sum them, and convert back to dB.

Worked Example: Two 80 dB Sources

L = 10 × log₁₀(10⁸ + 10⁸) = 10 × log₁₀(2 × 10⁸) = 80 + 3.01 = 83.0 dB

Two equal sources add only 3 dB.

Quick Mental-Math Rules

A whisper next to a jet engine adds essentially nothing — the larger source dominates.

Why dB Is Logarithmic

Human hearing runs from a threshold of 20 µPa up to roughly 200 Pa, where damage starts. That is a ratio of ten million to one, so seven orders of magnitude in pressure, or fourteen in intensity, since intensity goes as pressure squared.

Written out in pascals those numbers are unusable. The logarithm compresses the same span into a 0–140 scale, and 20 × log₁₀(200 ÷ 0.00002) lands on exactly 140 dB, which is where the top of that scale comes from.

Common Levels

Subtracting Backgrounds

To remove a known background level B from a measured total M:

L_signal = 10 × log₁₀(10^(M / 10) − 10^(B / 10))

Useful for environmental noise — subtract background traffic from a peak measurement to isolate the source. The signal must be at least 3 dB above the background for this to be reliable.

A-Weighting

Most regulations use dB(A) — sound levels weighted to match human hearing’s frequency response. The combining math is identical for dB(A); just keep the weighting consistent across all your inputs.

Worked Example: Factory Floor

Three machines at 88, 90, and 85 dB(A):

• 10⁸·⁸ + 10⁹·⁰ + 10⁸·⁵ = 6.3096 × 10⁸ + 1.0000 × 10⁹ + 3.1623 × 10⁸ = 1.9472 × 10⁹
• L = 10 × log₁₀(1.9472 × 10⁹) = 92.89 dB(A)

Keep four significant figures through the middle of that. Round the sum to 1.95 × 10⁹ and you get 92.90, which is close enough for a report but will not match the calculator above.

The combined floor is 92.89 dB(A). That clears the 85 dB NIOSH recommended limit and the 90 dB OSHA permissible limit, so hearing protection is required, not merely advisable.

Notice what the 90 dB machine is doing. On its own it would read 90.0, so the other two together add just 2.89 dB on top of it.

That has a direct consequence for where the money goes. Silence one machine at a time and the floor falls by:

Retiring the quietest machine buys you three quarters of a decibel, which nobody in the room will notice. Retiring the loudest buys four times as much and drops the floor under the 90 dB OSHA limit on its own. Noise control almost always starts with the biggest offender, and the arithmetic above is why.