Formula
A decibel is ten times the log of a power ratio, or twenty times the log of a pressure ratio. For sound pressure level in air the reference is 20 µPa, so dB SPL = 20 log10(p / 20 µPa). The numbers on a meter are already logarithms. Adding them as if they were litres double-counts the log.
L = 10 log10( Σ 10^(Li/10) )
Lcoherent = 20 log10( Σ 10^(Li/20) )
L2 = L1 + 20 log10(r1 / r2)
Incoherent and coherent sums
Uncorrelated sources, two talkers, two amplifiers, traffic plus a fan, add as energy. The default on this page is that sum. Two equal levels are about +3.01 dB. A level 10 dB below another adds about 0.4 dB, so the louder one dominates. The coherent form adds the pressures in phase. It is higher, about +6.02 dB for two equal sources, and it is only right when the sources are phase-locked at the listening point. That is uncommon outdoors. It can happen with identical drivers in a controlled array. The checkbox is off unless you turn it on.
Inverse square, and why a room is different
Doubling the distance from a point source in a free field multiplies pressure by 1/2, which is −6.02 dB. Ten times the distance is −20 dB. The table under the result lists the level at 1×, 2×, 4×, 8×, and 10× the first distance. Indoors, near a wall, or for a line source such as a road or a long array, the slope is shallower. A line source is often nearer −3 dB per doubling. This mode does not apply that slope. It is an outdoor free-field point source, with no room reflections.
Several speakers at one seat
Each speaker is moved from its reference distance to the listener with the same 20 log10 term, then the arrivals add with the incoherent sum. A trim is a dB offset you already know, such as a gain difference, applied before the distance term. N identical speakers at the same distance are one speaker’s level plus 10 log10(N). Four is about +6.02 dB. That is not twice as loud. A common rule of thumb is that +10 dB sounds about twice as loud, while +3 dB is about twice the acoustic power. Keep those two ideas apart.
Use a calibrated meter when the number has to be real. This page combines levels you type. It does not record a room. OSHA and NIOSH publish occupational noise exposure limits. Those limits are outside this calculator: it does not compute a noise dose, a time-weighted average, or a hearing-damage risk, and it will not tell you a level is safe.
Worked examples
Two incoherent 80 dB sources. The sum is 83.01 dB. The coherent checkbox on the same pair is 86.02 dB.
90, 85, and 80 dB. The incoherent sum is 91.51 dB.
Four identical 85 dB sources. 85 + 10 log10(4) is 91.02 dB. Ten identical 70 dB sources are 80.00 dB.
90 dB at 1 m. 2 m is 83.98 dB, 4 m is 77.96 dB, and 10 m is 70.00 dB. 94 dB at 3 ft is 81.96 dB at 12 ft, which is four times the distance and about −12.04 dB.
Two speakers, each 88 dB at 1 m. The listener is 2 m from the first and 4 m from the second. The arrivals are 81.98 dB and 75.96 dB. The incoherent sum is 82.95 dB.
Reference
Same formulas as the examples. Levels in dB. Distances in one unit inside each row.
| Case | Result |
|---|---|
| 80 + 80, incoherent | 83.01 dB |
| 80 + 80, coherent | 86.02 dB |
| 90 + 85 + 80 | 91.51 dB |
| Four × 85 | 91.02 dB |
| Ten × 70 | 80.00 dB |
| 90 dB at 1 m, then 2 / 4 / 10 m | 83.98 dB · 77.96 dB · 70.00 dB |
| 94 dB at 3 ft, then 12 ft | 81.96 dB |
| 88 dB at 1 m, listener at 2 m and 4 m | 81.98 dB · 75.96 dB · 82.95 dB |
Questions
How do you add decibels together?
You do not add the numbers. Uncorrelated sources add as energy: 10 log10 of the sum of 10^(Li/10). Two incoherent 80 dB sources are 83.01 dB, not 160. 90, 85, and 80 dB add to 91.51 dB. Equal levels are about +3 dB. A source 10 dB quieter barely moves the total.
How much does sound drop with distance?
Outdoors, a point source in a free field drops 20 log10 of the distance ratio. That is -6.02 dB per doubling and −20.00 dB per ten times the distance. 90 dB at 1 m is 83.98 dB at 2 m, 77.96 dB at 4 m, and 70.00 dB at 10 m. 94 dB at 3 ft is 81.96 dB at 12 ft.
How many dB is twice as loud?
Loudness and power are different. A rough rule for perceived loudness is that +10 dB sounds about twice as loud. +3 dB is about twice the acoustic power, which is what two equal incoherent sources do, and it does not sound twice as loud. This page does not turn a level into a loudness verdict.
Can I add speaker SPL ratings?
Only after you put them at the same distance. A sensitivity is a level at a stated distance, often 1 m. Two speakers, each 88 dB at 1 m, with the listener 2 m from one and 4 m from the other, arrive at 81.98 dB and 75.96 dB. The incoherent sum is 82.95 dB. N identical speakers at one distance add 10 log10(N), so four identical sources are about +6 dB, not twice as loud.
What is dB vs dB SPL vs dB(A)?
A decibel is a logarithmic ratio. dB SPL states the ratio against 20 µPa, the reference sound pressure in air. dB(A) is that level after an A-weighting filter, which roughly follows quiet-hearing sensitivity. C-weighting is flatter and is used for peaks. This page does not apply A, B, or C curves. Weighting needs the spectrum, and a single broadband number does not have one.
Does doubling the speakers double the loudness?
No. Two equal incoherent sources are about +3 dB, 83.01 dB from 80 dB. Doubling again, four sources, is 91.02 dB from 85 dB. Ten identical 70 dB sources are 80.00 dB. Perceived doubling is closer to +10 dB. A coherent pair, phase-locked at the seat, would be 86.02 dB instead of 83.01 dB, and that condition is rare outdoors.
Why is indoor falloff not −6 dB per doubling?
The −6.02 dB figure is spherical spreading from a point source with no reflections. A room adds reflections, so the level falls less once you are out of the near field, and it depends on the surfaces. A line source, such as a long array or a road, is closer to −3 dB per doubling. This distance mode does not model rooms or line sources.
Sources
- Lawrence E. Kinsler, Austin R. Frey, Alan B. Coppens, and James V. Sanders, Fundamentals of Acoustics. Level addition and spherical spreading.
- Leo L. Beranek and Tim J. Mellow, Acoustics: Sound Fields and Transducers. Sound pressure level and source combination.
- IEC 61672 and ANSI S1.4, sound level meters. The reference pressure used here is 20 µPa. A-weighting and C-weighting are defined there. This page does not apply them.
- OSHA noise exposure and NIOSH noise criteria are external references only. This calculator does not implement a dose, a time-weighted average, or a hearing-protection rating. osha.gov/noise.