Formula
Formula used
\[ L_{\text{total}} = 10 \log_{10} \left( 10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + \ldots + 10^{\frac{L_n}{10}} \right) \]
What the symbols mean
- L_total — resulting total sound level (dB)
- L₁, L₂, …, Lₙ — individual source levels to combine (dB)
Inputs
Identical sources
Combine several sources at the same level, then insert the result into the expression above.
Result
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Understand the theory — physics concept and calculationsinteractive
The first reflex to build: decibels don't add up like ordinary numbers. Two 80 dB machines side by side don't make 160 dB — they make 83 dB. Why? Because the decibel is a logarithmic scale: what adds up is acoustic energy, not the levels. Play with the sliders below to feel it.
What is a decibel?
The sound pressure level compares an RMS pressure \(p\) to a reference pressure \(p_0 = 2{\times}10^{-5}\ \text{Pa}\) (the hearing threshold at 1 kHz):
The factor 20 comes from the square: the ear (and physics) responds to energy, proportional to the square of pressure. That is exactly why two sounds add up in energy, not in pressure.
The addition formula
To combine \(n\) uncorrelated levels (independent sources), convert each level back to energy \(10^{L_i/10}\), sum, then return to decibels:
This is the formula the calculator above uses. Subtraction (removing background noise) follows the same logic with a "−" sign.
The addition chart (the field reflex)
In the field you don't always have a calculator. Acousticians use a shortcut: look at the difference between the two levels, and add a small correction to the louder one. Move the slider:
- 0 dB gap (equal sources) → +3 dB.
- 6 dB gap → +1 dB.
- ≥ 10 dB gap → +0.4 dB, negligible: the quiet source "vanishes" behind the loud one.
Practical consequence: to cut an overall noise, there's no point treating a source 10 dB below the dominant one. Tackle the loudest first.
Subtraction: removing background noise
You measure 75 dB with the machine running, and 69 dB of background (machine off). The level due to the machine alone is not 75−69 dB, but:
That is ≈ 73.7 dB. Safety rule (ISO): if the measurement-to-background gap is below 3 dB, the background dominates and the measurement is unusable.
Coherent sources: when the rule breaks
Energetic summation assumes uncorrelated sources (independent noises). For two coherent sounds of the same frequency (a duplicated loudspeaker, in-phase waves), the pressures add instead: two identical in-phase sources give +6 dB (not +3), and in anti-phase… silence. That's the whole principle of interference and active noise control.
dB, dBA: a nuance that matters
The addition is identical in dB or dB(A) — as long as you never mix the two. dB(A) first applies a frequency weighting that mimics the ear's sensitivity. Add dB(A) with dB(A), or dB with dB, never one with the other. See the other tools →
Worked examples
| Calculation | Result | Reading |
|---|---|---|
| 50 + 50 | 53.0 dB | two equal sources → +3 dB |
| 80 + 74 | 81.0 dB | 6 dB gap → +1 dB |
| 85 + 70 | 85.1 dB | 15 dB gap → the quiet one is negligible |
| 60 + 60 + 60 | 64.8 dB | three equal sources → +10·log 3 ≈ +4.8 dB |
- Adding arithmetically: 50 + 50 = 100 dB. Wrong → 53 dB.
- Averaging: (80+74)/2 = 77 dB. Wrong — it's an energy sum, not a mean → 81 dB.
- Mixing dB and dB(A) in the same sum.
- Forgetting that background subtraction is invalid when the gap is too small (< 3 dB).
Related tools
Sources : J.-C. Pascal, Vibrations et Acoustique (ENSIM, Le Mans Université); D. A. Bies & C. H. Hansen, Engineering Noise Control; L. L. Beranek, Noise and Vibration Control; M. Bruneau, Manuel d'acoustique fondamentale; ISO 1996-1.