Decibel Sum
Calculator
Results
- Combined level (dB)
- 83.010299
- Increase over the louder source (dB)
- 3.010299
- Difference between the levels (dB)
- 0
Music and audio results
| Combined level (dB) | 83.010299 |
| Increase over the louder source (dB) | 3.010299 |
| Difference between the levels (dB) | 0 |
formula-map diagram
- Combined level (dB)
- 83.010299
- Increase over the louder source (dB)
- 3.010299
- Difference between the levels (dB)
- 0
Musical and acoustic relationship
Formula
L = 10 × log₁₀(10^(L₁÷10) + 10^(L₂÷10))= 83.01029995664
Note
This result is a simplified model: it applies the displayed standard formula to the values you entered, assuming twelve-tone equal temperament, a speed of sound of 343 m/s in dry air at 20 °C, an ideal free field with no reflections or air absorption, purely resistive speaker loads and Sabine's diffuse-field assumption. Real rooms, instruments, codecs and amplifiers depart from these idealisations, so measure with proper instruments for critical work.
More in Music and audio
See all →Frequently asked questions
Why can't you just add two decibel values together?+
Decibels are a logarithmic representation of power or intensity, so combining two sound sources means adding their actual linear powers first and then converting the sum back to decibels, not adding the dB figures directly. Two 70 dB sources combined give about 73 dB, not 140 dB.
What's the formula for summing two decibel levels?+
The calculator converts each dB value back to linear power with 10^(dB/10), adds the linear powers together, then converts the total back to decibels with 10 x log10(sum). This correctly reflects how sound pressure levels physically combine in the air.
Why does combining two equal sound sources add only about 3 dB, not double the number?+
Two identical sources double the total power, and doubling power corresponds to +3 dB (10 x log10(2) ≈ 3.01), which is why two speakers each playing 80 dB together produce roughly 83 dB, not 160 dB. This 3 dB rule is one of the most useful shortcuts in acoustics and noise assessment.
Does the gap between two very different dB levels matter for the result?+
Yes, when one source is much louder than the other, say a 20 dB gap, the quieter source contributes almost nothing to the combined total, which ends up barely above the louder source's level alone. This matches real-world experience: a whisper next to a jackhammer doesn't meaningfully change the perceived noise level.
Where is this calculation actually used in practice?+
Noise assessments, environmental impact studies, and live sound planning all rely on this kind of summation to predict combined noise from multiple machines, speakers, or traffic sources, since regulatory noise limits are expressed in dB and require correct physical combination, not naive addition.