Short answer: You can’t add decibels directly because the scale is logarithmic. Convert each level to energy, add, then convert back: L = 10·log10(10L1/10 + 10L2/10 + …). Two equal sources add 3 dB, so 60 dB + 60 dB = 63 dB, not 120 dB. Ten equal sources add 10 dB, and a source 10 dB quieter adds only about 0.4 dB.
Adding decibels trips up almost everyone the first time. Two machines at 80 dB don’t make 160 dB; they make 83 dB. This guide gives the exact formula, a quick table you can use in your head, the rule for many equal sources, how to subtract background noise from a measurement and how to average decibel readings correctly, with worked examples throughout.
Why You Can’t Just Add Decibels
A decibel value is a logarithm of an energy ratio (see what a decibel is). Each 10 dB step multiplies the energy by 10, so the numbers compress a huge range into a short scale, as our guide to the logarithmic decibel scale explains. Sound energies from independent sources add; their decibel values don’t. To combine levels you first undo the logarithm, add the energies, then take the logarithm again.
The Decibel Addition Formula
For uncorrelated sources (different machines, voices or vehicles), the total level is:
Ltotal = 10 · log10(10L1/10 + 10L2/10 + … + 10Ln/10)
- Divide each level by 10 and raise 10 to that power. For 60 dB: 106 = 1,000,000.
- Add the results. Two sources at 60 dB: 2,000,000.
- Take log10 and multiply by 10: 10 × log10(2,000,000) = 63.0 dB.
The same works for sound pressure level in dB SPL, for dB(A) readings and for electrical power levels in dBm (see dB vs dBm vs dBW). The decibel calculator does it for up to many sources at once.
Quick Method: The Difference Table
For two levels, take the difference between them and add the matching amount to the louder one:
| Difference between the two levels | Add to the higher level |
|---|---|
| 0 dB | +3.0 dB |
| 1 dB | +2.5 dB |
| 2 dB | +2.1 dB |
| 3 dB | +1.8 dB |
| 4 dB | +1.5 dB |
| 5 dB | +1.2 dB |
| 6 dB | +1.0 dB |
| 8 dB | +0.6 dB |
| 10 dB | +0.4 dB |
| 15 dB or more | about +0.1 dB or less |
For more than two sources, combine them in pairs. Example: 85, 82 and 78 dB. First 85 and 82 differ by 3 dB, so 85 + 1.8 = 86.8 dB. Then 86.8 and 78 differ by about 9 dB, adding about 0.5 dB, which gives 87.3 dB. The full formula gives the same 87.3 dB. Notice that the 78 dB source barely matters: the loudest source dominates.
Adding Many Equal Sources
For n identical sources the rule is simply +10·log10(n):
| Number of equal sources | Increase over one source |
|---|---|
| 2 | +3.0 dB |
| 3 | +4.8 dB |
| 4 | +6.0 dB |
| 5 | +7.0 dB |
| 10 | +10.0 dB |
| 100 | +20.0 dB |
This is why ten people talking at 60 dB each give about 70 dB, not 600 dB, and why a busy open-plan office or a lively classroom is louder than any single voice but never as loud as the arithmetic suggests. It also works in reverse: halving the number of equal sources, such as the traffic on a road, lowers the level by only 3 dB.
Subtracting Background Noise
When you measure a machine in a noisy place, the reading includes the background. To remove it, measure the total (Lt) with the machine running and the background (Lb) with it off, then:
Lsource = 10 · log10(10Lt/10 − 10Lb/10)
Example: 65 dB total with 60 dB background gives 63.3 dB for the machine alone. As a table:
| Total minus background | Subtract from the total |
|---|---|
| Less than 3 dB | Unreliable: the source is buried in the background |
| 3 dB | −3.0 dB |
| 4 dB | −2.2 dB |
| 5 dB | −1.7 dB |
| 6 dB | −1.3 dB |
| 7 dB | −1.0 dB |
| 8 dB | −0.8 dB |
| 9 dB | −0.6 dB |
| 10 dB or more | −0.5 dB or less: usually ignored |
Measure the background first with the background noise test. If the difference is under 3 dB, move closer to the source or wait for a quieter moment rather than trusting the correction.
Averaging Decibels: Energy vs Arithmetic
Averaging has the same trap. The arithmetic mean of 70 dB and 80 dB is 75 dB, but the energy average is:
Lavg = 10 · log10((107 + 108) ÷ 2) = 77.4 dB
The louder reading dominates, just as in addition. When readings lie within a few dB of each other, such as repeated measurements of the same source, the arithmetic mean is close enough. When levels vary widely over time, use the energy average weighted by time, called Leq; the noise monitor calculates it for you, and the noise exposure calculator uses the same principle to combine a working day of different levels.
Worked Examples and Common Mistakes
- Two lawn mowers at 90 dB each: 93 dB. That is double the energy, which halves the safe exposure time.
- A machine at 88 dB beside one at 85 dB: the difference is 3 dB, so the total is 89.8 dB.
- 60 dB + 50 dB: 60.4 dB. The quieter source adds almost nothing.
- Mixed weightings: don’t add a dB(A) reading to a dB(C) reading; convert both to the same weighting first (see dB vs dBA).
- Identical signals: the formula assumes independent sources. Two speakers playing the same signal are correlated and can add up to +6 dB at some spots and cancel at others.
Want to hear what these differences sound like? The volume level comparator plays steps of 3, 6 and 10 dB, and the SPL converter turns decibels into pascals and back. For other decibel units, see the decibel units guide; to take good readings in the first place, read how to measure decibels or use our free decibel meter.
Frequently Asked Questions
What is 60 dB + 60 dB?
63 dB. Two equal, independent sources always add 3 dB to the level of one.
What is 50 dB + 60 dB?
About 60.4 dB. When one source is 10 dB quieter, it adds only about 0.4 dB.
Does doubling the sound add 3 dB or 6 dB?
Doubling the energy (two identical sources) adds 3 dB. Doubling the sound pressure adds 6 dB. Sounding twice as loud takes about 10 dB.
How do you subtract decibels?
Convert both to energy, subtract, and convert back: 10·log10(10Lt/10 − 10Lb/10). The result is only reliable when the total is at least 3 dB above the background.
How do you add decibels on a calculator?
Use the 10x and log keys as in the formula above, or enter the levels in the add tab of our decibel calculator.
Addito is an audio analysis and sound measurement writer specializing in decibel testing, noise level analysis, sound frequency measurement, and audio engineering tools for creators, audio professionals, students, and everyday users. He creates practical content focused on sound measurement, hearing safety, microphone testing, and acoustic analysis tools.