Decibel Addition Calculator
Combined noise of two or three sources in dB, with gain over loudest.
What it does
Decibels compress huge intensity spans into small numbers, so adding them arithmetically explodes the answer. Two 80 dB machines do not make 160 dB; they double intensity, which is 3.01 dB, landing at 83.01 dB.
The tool above takes two or three source levels and sums their powers inside the log. It returns the combined level, the gain over the loudest source, and the intensity multiple. The default twin 80 dB pair gives 83.01 dB at plus 3.01 dB and 2 x intensity.
Sound texts define level as 10 times log10 of intensity over the hearing threshold, with the doubling proof worked beside it: twice the intensity is 10 log10 of 2, which is 3.01 dB. Federal noise reviews print the same power sum form with twin 93 dB sources landing near 96 dB.
The loudest source rules every mix. A 10 dB gap contributes under half a decibel, so quiet partners vanish perceptually while equal partners lift audibly. Hearing guidance keys on the total: repeated 85 dB days damage, and 70 dB days stay safe.
How to use
- Pick two or three sources.
- Type each level in dB at the same spot and weighting.
- Read combined level first, gain beside it.
- Judge risk on the total, not the loudest alone.
- Expect near 3 dB for twins, near zero for mismatches.
- Recheck when distances or barriers change per source.
Formula
- Li
- Each source level in dB, same weighting and spot.
- gain
- Lift over the single loudest source.
- ratio
- Combined intensity over loudest intensity.
Coherent tones can interfere and break power summation; incoherent machine and crowd noise follows it. Equal N sources add 10 log10 of N.
Worked example
Example: 80 plus 80 dB
Defaults: two sources at 80 dB each.
- Powers: 10^8 is 100,000,000 per source.
- Sum: 100,000,000 + 100,000,000 = 200,000,000.
- Log: log10 of 200,000,000 is 8.30103.
- Total: 10 x 8.30103 = 83.01 dB.
- Gain: 83.01 minus 80 is plus 3.01 dB, ratio 2 x.
- Tool shows 83.01 dB, +3.01 dB, 2 x.
Reference table
| Level or rule | Value | Meaning |
|---|---|---|
| 0 dB | 1e-12 W/m2 | Hearing threshold at 1000 Hz |
| 60 dB | Normal conversation | Everyday speech band |
| 100 dB | Noisy factory | 8 hour damage zone |
| 120 dB | Rock concert | Pain starts near here |
| 140 dB | Jet at 30 m | Immediate harm zone |
| Twin sources | Plus 3.01 dB | Intensity doubles |
| 10 to 1 intensity | Plus 10 dB | Ten times the power |
Limits
- Incoherent sources assumed; pure tones interfere.
- Same weighting and distance required per source.
- Perception differs from physics near thresholds.
- Damage math needs dose time, not just level.
Common mistakes
- Adding 80 and 80 as 160 dB.
- Averaging decibels arithmetically.
- Mixing dB with dBA across sources.
- Measuring each source at a different distance.
- Treating 3 dB as nothing; it is double power.
Try it yourself
Quick checks. Answers sit tucked under each question.
Two 90 dB machines?
93.01 dB, plus 3.01 over either alone.
85, 88, and 90 dB together?
92.89 dB, plus 2.89 over the 90.
110 plus 90 dB?
About 110.04 dB; the 90 nearly vanishes.
Questions
What is 80 plus 80 dB?
83.01 dB: double intensity is plus 3.01 dB.
Why not 160 dB?
Decibels are logarithmic; powers add inside the log, not the numbers outside.
What do twins add?
3.01 dB for two equal, 4.77 for three equal, 6.02 for four.
When can I ignore a source?
Ten or more dB under the leader it adds under half a decibel.
dB or dBA here?
Math is identical; keep one weighting across all sources.
When does damage start?
Repeated 85 dB days harm; keep routine exposure at 70 dB or below.
Sources
- CDC Stacks: Noise Exposure and Control (NIOSH)
- OpenStax College Physics: Sound Intensity and Sound Level