Station Audio

Decibel calculator

Four everyday decibel sums: adding sources, removing background noise, converting ratios, and allowing for distance. Every box updates as you type.

1. Add sound levels

Combined level of unrelated sources

93.0 dB

2 sources. If they were identical signals exactly in phase, the most they could reach is 96.0 dB. The loudest source alone is 90.0 dB, so the others add 3.0 dB.

2. Subtract background noise

The source alone is 76.7 dB.

3. Ratio and decibels

Edit either box; the other follows.

4. Level at another distance

About 81.9 dB (free field, point source).

Ratio to decibels

RatioAs power (10 log)As voltage / pressure (20 log)
1.122×0.50 dB1.00 dB
1.259×1.00 dB2.00 dB
1.413×1.50 dB3.00 dB
2×3.01 dB6.02 dB
3.162×5.00 dB10.00 dB
4×6.02 dB12.04 dB
10×10.00 dB20.00 dB
100×20.00 dB40.00 dB
1000×30.00 dB60.00 dB

How long is safe? Occupational noise limits

Daily exposure time at an A-weighted level before reaching each limit. NIOSH's recommended limit is the more protective of the two and is the one hearing specialists generally point to; OSHA's is the US legal workplace limit.

LevelNIOSH REL (85 dBA, 3 dB rate)OSHA PEL (90 dBA, 5 dB rate)
85 dBA8 hno limit below 90
88 dBA4 hno limit below 90
90 dBA2.5 h8 h
91 dBA2 h7 h
94 dBA1 h4.6 h
95 dBA48 min4 h
97 dBA30 min3 h
100 dBA15 min2 h
103 dBA7.5 min1.3 h
106 dBA3.8 min52 min
110 dBA1.5 min30 min

These are workplace criteria for averaged daily exposure, not a guarantee of safety for any one person. Rehearsals, gigs and headphone listening regularly exceed them. If you work around loud sound, use hearing protection and get your hearing checked by a professional.

How the calculations work

A decibel is ten times the base-10 logarithm of a power ratio. Because it is logarithmic, levels cannot be added directly: each has to be converted back to power, summed, and converted again.

Worked example. A guitar amp at 96 dB and a bass amp at 93 dB, measured separately from the same spot: 109.6 + 109.3 = 3.98 × 109 + 2.00 × 109 = 5.98 × 109, and 10 × log10 of that is 97.8 dB. The quieter amp adds only 1.8 dB. A useful rule of thumb follows: a source 10 dB below another adds about 0.4 dB, and one 20 dB below adds almost nothing.

For background noise, a machine measures 78 dB with the room at 72 dB. The machine alone is 10 × log10(107.8 − 107.2) = 76.7 dB. If the total is less than 3 dB above the background, the answer is very sensitive to small measurement errors, and acoustic measurement standards generally require the source to stand several decibels above the background before they allow a correction at all.

Where it stops being reliable

All of these formulas assume the levels you enter use the same weighting (A, C or Z) and the same reference. Adding an A-weighted level to a C-weighted one gives a meaningless number. The in-phase sum is an upper limit that real rooms rarely reach across a range of frequencies: two speakers playing the same signal add by 6 dB at low frequencies, where they are close together relative to the wavelength, but closer to 3 dB at high frequencies, where their outputs arrive with varying phase.

The distance rule holds only outdoors and away from surfaces. In a room, the level falls with distance only until the reverberant field takes over, and after that it hardly changes. The room mode calculator covers the related problem of why some bass notes are louder than others in one spot.

Common questions

5 answers
Two 90 dB sources: is that 180 dB?

No. Decibels are logarithmic, so levels add as powers. Two equal, unrelated sources give 3 dB more than one: 93 dB. Ten of them give 10 dB more, 100 dB. Only when two signals are identical and exactly in phase, such as the same signal through two speakers heard at the same distance from both, can they reach 6 dB more, and that happens only at particular positions and frequencies.

When do I use 10 log and when 20 log?

Use 10·log10 for ratios of power or intensity: watts into a speaker, acoustic intensity, energy. Use 20·log10 for ratios of field quantities, whose square is proportional to power: voltage, current, sound pressure. Doubling voltage into the same load quadruples power, and both rules give the same answer: +6.02 dB.

How much louder is 10 dB?

Ten times the power, and roughly twice as loud to most listeners, although perceived loudness depends on frequency and level. 3 dB is double the power and a clearly noticeable but modest change; 1 dB is around the smallest change most people notice in a controlled comparison.

Can I measure sound levels with this page?

No. It calculates with numbers you give it and does not use the microphone. To measure you need a sound level meter; phone apps can be useful for rough readings but vary in accuracy, especially at high levels and low frequencies.

Does sound really drop 6 dB per doubling of distance?

Only in a free field from a small source: outdoors, away from reflecting surfaces. Indoors, reflections build up a reverberant level that stops falling beyond a certain distance. A long line source such as a busy road or a line array falls closer to 3 dB per doubling. Use the distance result as the best case for how much quieter it gets.

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