How to Add and Subtract Noise Levels Correctly

Why this matters

The number that gets argued over is almost never the raw meter reading. It is the source's own contribution, and that figure is always a subtraction: what you read with the thing running, minus what was already there. Do that subtraction without checking one quantity first and you will hand over a level that looks like a measurement and is actually a guess with two decimal places on it. The quantity is the margin between the two readings, and it decides whether you walk away with a number or with a bound. Those are different deliverables and they are argued differently.

The gate, stated once

The margin is the combined reading (source running, everything else normal) minus the background reading (source off, everything else identical). Compare that margin, per measurement position and per the band or overall figure you intend to report, against three zones.

Those zone boundaries are the widely used convention. The test method, ordinance or specification your result will be judged under states its own, and that one governs; if your report has a named method, read its rule rather than this table.

What must match before any arithmetic

Levels combine only when they are levels of the same thing. Five items, and a mismatch on any one makes the arithmetic meaningless rather than merely approximate.

1. Quantity. Both figures are sound pressure levels re 20 micropascals, or both are sound power levels re 1 picowatt. Never one of each.
2. Weighting. Both A-weighted, both C-weighted, or both unweighted. There is no conversion between them without the spectrum.
3. Bandwidth. Both overall, or both the same octave or third-octave band. An overall figure and a band figure do not subtract.
4. Time basis. Both equivalent-continuous over the same duration, or both the same time weighting (fast or slow), or both peak. A 5-minute equivalent-continuous level and a fast-response maximum are different quantities.
5. Position. Same microphone position, same height, same orientation. A background taken from a different spot is not the background of this reading.

The procedure

1. Fix and write the basis before the meter comes out: quantity, weighting, bandwidth, time basis, position and height. Every figure that follows carries it.
2. Check the calibrator before and after the whole set, not between readings, and record both. A drift check that fails voids the set; the record that makes this auditable is its own card.
3. Take the combined reading with the source in its normal operating state.
4. Take the background with the source off and nothing else changed. If turning the source off forces a process change, stop the process too and say so; a background measured under different process conditions is not this reading's background.
5. Compute the margin and locate it in the zone table before doing anything else.
6. Apply the correction, or refuse to. Subtract from the combined reading:

1. Repeat the margin check per band if the decision the number feeds is a per-band decision. A healthy overall margin routinely hides a band with no margin at all.
2. Report the basis with the number, including whether a correction was applied or declined.

Adding levels together, rather than subtracting, uses the mirror of that table and is owned by the sibling card on why decibels do not add arithmetically; use it there rather than a second version here.

Case one: the dust collector, which resolves to a measurement

A shop wants the new dust collector's own contribution at the operator position, because the operator's exposure documentation has to attribute it.

Basis, held on every figure: A-weighted, overall, 5-minute equivalent-continuous sound pressure level (LAeq,5min) re 20 micropascals, microphone on a stand at 1.5 m above the floor at the operator position.

• Collector running, shop otherwise normal: 82.0 dB
• Collector off, shop otherwise identical: 74.0 dB

Background conditions, printed as its own line. The background was taken with the dust-generating operation stopped, not merely with the collector switched off. Running a dust-generating process with its capture down is an inhalation exposure, and respirable crystalline silica is a regulated exposure under 29 CFR 1910.1053 in general industry and 29 CFR 1926.1153 in construction, with wood dust carrying its own respiratory controls. The measurement is not worth an exposure, and stopping the process is also the only way the background stays comparable.

Margin: 82.0 minus 74.0 = 8.0 dB, which lands in the middle zone. A correction applies and is not declined.

Correction: 0.7 dB from the table. Collector contribution = 82.0 minus 0.7 = 81.3 dB LAeq,5min re 20 micropascals at that position.

Sensitivity, printed because the zone table's whole justification is this. Move the background by half a decibel in either direction, to 73.5 or 74.5, and the answer moves between 81.3 and 81.2. A 1.0 dB span in the input produces a 0.2 dB span in the output. The correction is stable because the margin is comfortable.

Error character, printed because a magnitude with no character cannot enter arithmetic. Both readings came from the same instrument minutes apart. A sound level meter's class tolerance is a worst-case bound over frequency, not an independent random spread, and for one instrument at one frequency it behaves largely as a fixed offset. A fixed offset common to both readings cancels in their difference, so the 8.0 dB margin and the 0.7 dB correction are more trustworthy than either absolute figure. What does not cancel is the absolute 81.3, which still carries the instrument's own bound. Report the bound as a bound, with one inequality sign, never as a plus-or-minus interval.

Per-band check, because the treatment decision is per band. In the 500 Hz octave band the background is 66 dB and the combined 78 dB, a 12 dB margin, so no correction and a solid figure. In the 63 Hz octave band the background is 68 dB and the combined 69 dB, a 1 dB margin. The overall correction of 0.7 dB says nothing about that band, and the 63 Hz result is a bound, not a measurement. A shop that read only the overall would have specified low-frequency treatment against a number it never had.

Case two: the transfer pump, which resolves to a bound

Same shop, same position, same basis, a small transfer pump.

• Pump running, shop otherwise normal: 76.0 dB
• Pump off, shop otherwise identical: 74.0 dB

Margin: 76.0 minus 74.0 = 2.0 dB, below the 3 dB floor.

What the table would have produced, and why it is refused. Energy subtraction at a 2.0 dB margin returns 71.7 dB, a confident-looking figure. Move the background half a decibel, to 73.5 or 74.5, and that answer swings between 72.4 and 70.7, a 1.8 dB span from a 1.0 dB input. The subtraction amplifies input error rather than absorbing it, which is precisely what the floor exists to stop.

What is reported: the pump's contribution at that position is not greater than 73.0 dB LAeq,5min re 20 micropascals, one inequality sign, no interval. The pump is quiet enough that this room cannot resolve it.

What would change the answer. Two things and only two: measure closer to the pump, where its own contribution rises while the background does not, until the margin clears 3 dB; or reduce the background by stopping other equipment, which changes what the number means and has to be said. Averaging more readings does not help, because the limit here is not random scatter, it is that the quantity is buried.

Verifying you got it right

Read your own report back and confirm four things.

Every number carries its basis. Quantity, weighting, bandwidth, time basis, position. A figure missing any one of them is not a measurement and cannot be defended.

The correction is visible, including when it was declined. A report that shows 82.0 and 81.3 with the 0.7 named is auditable. One that shows only 81.3 cannot be checked by anyone, including you in six months.

Bounds are written as bounds. "Not greater than 73.0" and "71.7 plus or minus 2" are not two ways of saying the same thing. The second implies the true value is as likely to be above as below, which at a 2 dB margin is false.

The arithmetic closes forward. Take your reported source level, re-add the background by energy, and confirm you land back on the combined reading. Case one: recombining 81.3 with 74.0 returns 82.0, which is the reading that was taken. It closes. If a forward check does not return the reading you actually took, the correction went the wrong way, which is the most common single error in this whole procedure.

Hearing protection where you must raise your voice to be heard at arm's length, and note it does not change what the microphone reads. Place the microphone on a stand outside the plane of any rotating component, with guards in place per 29 CFR 1910.212(a)(1), never reaching past a guard to position it. Where a background reading requires stopping equipment, confirm with the owner of the load that the stop is permitted before it happens.

References

• 29 CFR 1910.95, Occupational noise exposure, including the monitoring requirements at (d)
• 29 CFR 1910.1053 in general industry and 29 CFR 1926.1153 in construction for respirable crystalline silica
• 29 CFR 1910.212(a)(1) for machine guarding around a microphone position
• The test method, ordinance or purchase specification your result will be judged under, in the edition it names, which owns its own background-correction rule
• See related: Why Decibels Do Not Add the Way Numbers Do; How to Take a Sound Measurement Somebody Else Can Repeat