Decibel addition calculator
Add sound levels
Levels from separate sources at the same spot. Enter two or more.
Sound level at a distance
A point source in a free field, with no walls or other reflecting surfaces nearby.
Octave bands to dBA
Pre-filled with the worked example from OTM Appendix B.5. Leave a band blank to skip it.
| Band (Hz) | Lp (dB) | A weight | dBA |
|---|---|---|---|
| 31.5 | −39 | 55 | |
| 63 | −26 | 69 | |
| 125 | −16 | 76 | |
| 250 | −9 | 86 | |
| 500 | −3 | 94 | |
| 1,000 | 0 | 97 | |
| 2,000 | +1 | 103 | |
| 4,000 | +1 | 98 | |
| 8,000 | −1 | 91 |
Formulas and sources
- Total L = 10 × log10(Σ 10^(Ln/10))
- Lp2 = Lp1 + 20 × log(d1/d2)
- LA = 10 × log10(Σ 10^((Lp + A)/10)), with A from the OTM B.5 table
The formula comes from
OSHA Technical Manual, Section III, Chapter 5 (Noise), Appendix B.3(opens ecfr.gov in a new tab)“Decibels are measured using a logarithmic scale, which means decibels cannot be added arithmetically. For example, if two noise sources are each producing 90 dB right next to each other, the combined noise sound pressure level will be 93 dB, as opposed to 180 dB. The following equation should be used to calculate the sum of sound pressure levels, sound intensity levels, or sound power levels: Total L = 10 x log10(Σ1n 10Ln/10)”
Source
OSHA Technical Manual, Section III, Chapter 5 (Noise), Appendix B.3(opens ecfr.gov in a new tab)“Difference Between Two Levels to Be Added | Amount to Add to Higher Level to Find the Sum: 0-1 dB | 3 dB; 2-4 dB | 2 dB; 5-9 dB | 1 dB; 10 dB | 0 dB. Example: There are three noise sources immediately adjacent to one another, each producing a sound pressure level of 95 dB. ... the sum will be 95 + 3 = 98 dB. The difference between 98 dB and the remaining noise source (95 dB) is 3, which means the sum will be 98 + 2 = 100 dB.”
The formula comes from
OSHA Technical Manual, Section III, Chapter 5 (Noise), Appendix B.6(opens ecfr.gov in a new tab)“If a sound is generated at a point source in a free field, meaning there are no walls or other obstructions, the sound pressure level, Lp, will be reduced by 6 dB each time the distance from the noise source is doubled. ... Lpd2 = Lpd1 + 20 × log(d1/d2) ... Lpd1 is 120 dBA, d1 is 50 ft, and d2 is 80 ft. Therefore, Lpd2 is 120 + 20 × log(50/80), which is 116 dBA.”
The formula comes from
OSHA Technical Manual, Section III, Chapter 5 (Noise), Appendix B.5(opens ecfr.gov in a new tab)“This is easily done by applying the A-scale correction factors for the nine standard octave center frequencies and combining the corrected values by decibel addition (see B.3 above). ... 31.5 | -39; 63 | -26; 125 | -16; 250 | -9; 500 | -3; 1,000 | 0; 2,000 | +1; 4,000 | +1; 8,000 | -1”
Source
OSHA Technical Manual, Section III, Chapter 5 (Noise), II.B.6 Sound Fields(opens ecfr.gov in a new tab)“The net result is a change in the intensity of the sound. The sound pressure does not decrease as rapidly as it would in a free field. In other words, it decreases by less than 6 dB each time the distance from the sound source doubles.”
FAQ
How do you add decibels?
Convert each level to relative energy, add, and convert back: Total L = 10 × log10(10^(L1/10) + 10^(L2/10) + …). That is the equation in OSHA Technical Manual Section III Chapter 5, Appendix B.3. Decibels can't be added arithmetically.
What do two 90 dB sources add up to?
93 dB, not 180 dB. Two equal sources always add about 3 dB, because doubling the sound energy raises the level by 10 × log10(2) ≈ 3.01 dB.
Is there a quick rule for adding decibels without a calculator?
OSHA's table adds to the higher level by the difference between the two: 0–1 dB apart add 3 dB, 2–4 dB apart add 2 dB, 5–9 dB apart add 1 dB, and 10 dB or more apart add nothing. Three 95 dB sources come to 98, then 100 dB this way. The exact equation gives 99.8 dB.
How much does sound drop with distance?
From a point source in a free field, about 6 dB each time the distance doubles: Lp2 = Lp1 + 20 × log(d1/d2). OSHA's example: 85 dBA at 100 ft is 79 dBA at 200 ft and 97 dBA at 25 ft. Indoors, reflections make the drop smaller than 6 dB.
How do you convert octave band readings to dBA?
Add the A-scale correction to each band (−39 at 31.5 Hz up to +1 at 2,000 and 4,000 Hz, per OTM Appendix B.5), then combine the corrected bands by decibel addition.
Combining levels gives the level at one location. For a worker's daily exposure over different levels and durations, use the noise dose and TWA calculator. To check hearing protectors against that TWA, use the NRR calculator. Every noise formula is also on the free ASP formula sheet. This tool is for study and estimation, not a substitute for a noise survey with a calibrated meter.