Case 1
- First level
- 60dB
- Second level
- 60dB
63.0103dB
Open with these valuesDecibel Sum Calculator
63.0103dB
Result: 63.0103 dBTwo sources of 60 dB together make 63.01 dB, not 120. Levels have to be taken back to intensities, added there, and turned into a level again. Two equal sources always add 3.01 dB; ten decibels apart, the quieter one adds only 0.41 dB.
Worked examples
Case 2
- First level
- 70dB
- Second level
- 60dB
70.4139dB
Open with these valuesCase 3
- First level
- 90dB
- Second level
- 80dB
90.4139dB
Open with these valuesHow it's calculated
L = 10 × log₁₀(10^(L₁ ÷ 10) + 10^(L₂ ÷ 10))
- StepEnter the first sound level in decibels.
- StepEnter the second level.
- ResultRead the combined level of both sources together.
What this number means
Decibels do not add
Two sources of 60 dB together make 63.0103 dB — not 120, and not 60 either. The levels have to be taken back to intensities, added there, and turned into a level again.
Two equal sources always add 3.0103 dB
The step does not depend on the level: 0 and 0 give 3.0103, 60 and 60 give 63.0103, 80 and 80 give 83.0103. Doubling the intensity is always the same 3.01 dB.
A much quieter source barely counts
Ten decibels below, the second source adds 0.4139 dB, so 70 and 60 come to 70.4139. Twenty decibels below it adds 0.0432 dB, which no measurement will separate from noise.
More than two sources: work in pairs
Combine the first two, then feed that total in against the third. Three sources of 60 dB give 63.0103 and then 64.7712 dB.
Commonly misread
Two speakers at 60 dB each make 120 dB.
They make 63.0103 dB. The decibel is a logarithm of an intensity ratio, and logarithms do not add linearly.
A 60 dB fan beside an 80 dB machine pushes the total well above 80 dB.
It adds 0.0432 dB, for 80.0432 dB together. Twenty decibels down, the quieter source is practically not there.
I need a reference pressure before I can add two levels.
Both levels carry the same reference, and it cancels when they are converted to intensities and back. The two decibel figures are all this calculation needs.
Reference table
| Two levels (dB) | Gap between them | Together (dB) |
|---|---|---|
| 0, 0 | Equal | 3.0103 |
| 60, 60 | Equal | 63.0103 |
| 70, 60 | 10 dB apart | 70.4139 |
| 80, 60 | 20 dB apart | 80.0432 |
| 90, 80 | 10 dB apart | 90.4139 |
Questions
Why don't decibels just add up?
The decibel is a logarithm of an intensity ratio, and logarithms do not add linearly. Adding the intensities and taking the logarithm afterwards is the only correct order.
What do two equal sources give?
Exactly 3.0103 dB more than one of them, whatever the level. Two lorries at 80 dB make 83.01 dB, and two at 60 dB make 63.01 dB.
How much does a much quieter source add?
Very little. Ten decibels below, it adds 0.41 dB; twenty decibels below, only 0.04 dB, which no measurement will separate from noise.
Do I need a reference pressure for this?
No. Both levels carry the same reference, and it cancels when they are converted to intensities and back.
Does this work for more than two sources?
Yes, by pairs. Combine the first two, then feed that total in against the third.
Sources and last check
Information, not professional advice.