Logarithmic sums
Decibel calculator
Decibels do not add like ordinary numbers: two 80 dB machines make 83 dB, not 160. Four calculators for the sums that come up most.
Add sound levels
Sources playing at the same time. Use the count for several identical ones.
4 sources together. The loudest alone is 85.0 dB, so the others add +2.8 dB.
Subtract background noise
Measure with the source on (total) and off (background) to find the source alone.
The background took 1.0 dB off the total.
Average sound levels
Paste readings separated by spaces, commas or new lines; the meter's CSV column works too.
Energy average of 6 levels, from 59.5 to 74.2 dB. The plain arithmetic mean would be 66.8 dB.
Level at a distance
Spreading in open air from a point source (a machine) or a line source (a busy road).
−20.0 dB from 1 to 10: about 6 dB per doubling of distance for a point source in the open.
The formulas behind the four panels
A decibel level is 10 × log10 of an energy ratio, so the sums happen on the energies. Adding: convert each level L to 10^(L/10), add, and convert back with 10 × log10. Two equal sources give +3 dB, ten give +10 dB, and a source 10 dB quieter than another adds only 0.4 dB.
Subtracting works the same way backwards: 10 × log10(10^(Lt/10) − 10^(Lb/10)). When the total is at least 10 dB above the background the correction is under half a decibel. Under 3 dB, the source is quieter than the background and the answer is too sensitive to trust; measure closer to the source or at a quieter time.
The energy average is what a sound level meter's Leq does: the loud moments dominate, so 90 and 60 dB average to 87 dB, not 75. Use it for readings of equal duration.
Distance: in open air, sound from a small source spreads over a sphere and drops 20 × log10(r2/r1), about 6 dB each time the distance doubles (the inverse square law). A long line such as a road or railway spreads over a cylinder and drops about 3 dB per doubling. Walls, ground, wind and air absorption change real results, often by several decibels.
Mix only levels with the same weighting: dBA with dBA, dBC with dBC.
Questions
How many decibels is twice as loud?
Doubling the sound energy adds 3 dB, which is a clear but modest change. Most people judge a sound about 10 dB higher as roughly twice as loud, and that takes ten times the energy: ten identical machines instead of one.
Can I add dBA readings from different machines?
Yes, as long as each was measured at the same spot and all are A-weighted. The sum estimates the level with everything running together. Adding a dBA reading to a dBC or unweighted one gives a number with no clear meaning.
Why does my measured level not drop 6 dB per doubling?
The rule needs open air, a small source and a listener far from reflecting surfaces. Indoors, reflections from walls and ceilings keep the level up away from the source, and close to a large machine you are in its near field, where the level changes less predictably.