Type a line (85 dB(A) + 88 dB(A) + 90 dB(A); total 92 dB background 86 dB; average 88 91 86 dB(A)) or fill in the fields: the line and the fields stay in step.
Enter sound level meter readings in dB or dB(A), and the calculator adds the levels of several sources, takes the background noise off a total, averages readings both on energy and as plain figures, labelled, and works out N identical sources or the level at another distance. Decibels add on energy, not as figures: 85 and 88 dB(A) together give 89.8 dB(A), not 173. It shows the working with your numbers, draws the levels and the result as bars on one scale, and gives a line you can copy or add to a request.
The unit stays as written: the calculator does not convert dB(A) to dB and does not add levels of different weightings. When the total is less than 3 dB above the background, it says that the source cannot be separated reliably. The level at a distance is worked out for a point source in a free field, and an engine room is not a free field. There are no noise limits and no hearing protection figures here: limits for noise on board are set by the noise code and the flag.
Each level becomes 10^(L/10), the values are added, and the sum goes back: L = 10 x log10 of the sum. 85, 88 and 90 dB(A) give 1.947 x 10^9, or 92.9 dB(A). The loudest source gives the most: the other two add only 2.9 dB to its 90 dB(A). N identical sources give L + 10 x log10(N): four of 82 dB give 88.0 dB.
Ls = 10 x log10(10^(Lt/10) - 10^(Lb/10)): a total of 92 dB with a background of 86 dB leaves 90.7 dB for the source. Under a 3 dB difference the source cannot be separated reliably: at a 2 dB difference a 0.5 dB error in the total moves the result by 1.4 dB. When the total is not above the background, the calculator gives no figure.
The energy average of 88, 91 and 86 dB(A) is 88.8 dB(A), the arithmetic one 88.3 dB(A): the calculator shows both, labelled. For a point source in a free field L2 = L1 - 20 x log10(r2 / r1): 94 dB at 1 m gives 82.0 dB at 4 m. In an engine room reflected sound adds to the direct sound, and further away the level falls less.
| Quantity | Relation | Note |
|---|---|---|
| Adding levels | L = 10 x log10(10^(L1/10) + 10^(L2/10) + ...) | on energy; 85 + 88 + 90 dB(A) = 92.9 dB(A) |
| Taking off the background | Ls = 10 x log10(10^(Lt/10) - 10^(Lb/10)) | Lt above Lb; under a 3 dB difference not reliable |
| Energy average | L = 10 x log10((10^(L1/10) + ... + 10^(Ln/10)) / n) | the level with the energy of all the readings |
| Arithmetic average | (L1 + ... + Ln) / n | the plain mean of the figures; never above the energy average |
| N identical sources | L + 10 x log10(N) | 2 sources add 3.0 dB; 10 add 10.0 dB |
| Distance | L2 = L1 - 20 x log10(r2 / r1) | free field, point source; 6.0 dB less per doubling |
All the levels in one calculation carry one weighting: dB(A) with dB(A), dB with dB. The calculator does not convert one weighting into another. Distances are in metres; feet are worked as 1 ft = 0.3048 m.
Adding levels on energy, L = 10 x log10 of the sum of 10^(Li/10), and the 10 x log10(N) for N identical sources are the standard acoustics relations: they are given in engineering references on adding decibels and in study material on workplace noise. Taking the background off on energy, and the rule that under a 3 dB difference the source cannot be separated reliably, are given in noise measurement guidance and in occupational hygiene study material; background correction tables start at a 3 dB difference. The energy average of readings is described in references on sound level calculations. The fall of 6 dB per doubling of distance holds for a point source in a free field; in a room the reflected sound adds to the direct sound, and beyond the critical distance the reflected field dominates.
On energy, not as figures. Each level becomes 10^(L/10), the values are added, and the sum goes back to decibels: L = 10 x log10(10^(L1/10) + 10^(L2/10) + ...). 85, 88 and 90 dB(A) give 3.162 x 10^8 + 6.310 x 10^8 + 1.000 x 10^9 = 1.947 x 10^9, and 10 x log10 of that is 92.9 dB(A), not 263. Two equal levels give 3.0 dB more than one of them.
Measure the total with the source running and the background with it stopped, then subtract on energy: Ls = 10 x log10(10^(Lt/10) - 10^(Lb/10)). A total of 92 dB with a background of 86 dB leaves 90.7 dB for the source: the background added 1.3 dB. When the total is less than 3 dB above the background, the source cannot be separated reliably: at a 2 dB difference a 0.5 dB error in the total moves the result by 1.4 dB. When the total is not above the background, nothing of the source can be worked out.
The energy average is the level with the same sound energy as all the readings together: 10 x log10 of the mean of 10^(L/10). The arithmetic average is the plain mean of the figures. For 88, 91 and 86 dB(A) the energy average is 88.8 dB(A) and the arithmetic one 88.3 dB(A). The arithmetic average is never above the energy one, and the gap grows with the spread of the readings; the calculator gives both, labelled.
N identical sources give L + 10 x log10(N): two give 3.0 dB more than one, four 6.0 dB more and ten 10.0 dB more. Four sources of 82 dB together give 88.0 dB. It holds for sources of the same level that run together and do not reinforce each other in step, as separate machines do.
For a point source in a free field, L2 = L1 - 20 x log10(r2 / r1): 6.0 dB less for each doubling of the distance. 94 dB at 1 m gives 88.0 dB at 2 m and 82.0 dB at 4 m. An engine room is not a free field: the sound reflected from the surfaces around adds to the direct sound, so further from the source the level falls less than this, and the figure is a free field estimate.
Levels in dB, or in dB(A), dB(C) or dB(Z) as the sound level meter shows them, and distances in metres or feet. The result keeps the unit of the readings: the calculator does not convert one weighting into another, and does not add levels of different weightings. It gives no noise limits and no hearing protection figures: limits for noise on board are set by the noise code and the flag.
The calculator works out sound levels. When parts are needed for the equipment you measured, send the line from the calculator with the equipment details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
