Sound Level and dB Addition Formulas

Sound level formulas: adding the levels of several sources in decibels and the fall in level with distance from a source in free field.

The formulas

Levels are in decibels (dB) and the distances r in the same unit. Decibels are logarithmic, so the levels are added as energies and not as numbers: two equal sources add 3 dB, and ten add 10 dB. The distance formula is for a point source in the open, with no reflection, which is a fair estimate for a generator or transformer away from walls. A hard wall nearby, a room or a screen changes the result, and the limit for noise depends on the rules for the site, so use your own limit. The figures here are examples.

Worked example: two sources of 80 dB

1. L = 10 × log10(2 × 10⁸) = 83.01 dB

Worked example: three sources of 70 dB

1. L = 70 + 10 × log10(3) = 74.77 dB

Worked example: 90 dB at 1 m, heard at 8 m

1. L2 = 90 − 20 × log10(8) = 71.94 dB

Level at distance for a source of 90 dB at 1 m

Frequently asked questions

Why do two equal sources add only 3 dB?

The sound energy doubles, and doubling the energy raises the level by 10 × log10(2) = 3 dB.

What does doubling the distance do?

In free field the level falls by about 6 dB, because the sound spreads over a sphere whose area grows with the square of the distance.

Can I add decibel values directly?

No. Convert them to energy, add and convert back, or use the equal-source shortcut.

Does the formula work indoors?

Not well. Reflections from the walls keep the level higher than the free-field value, so use a room model or measure.

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