Sound Level Addition Calculator

Why You Can’t Just Add Decibels Decibels are on a logarithmic scale: 60 dB + 60 dB ≠ 120 dB. Two equal sound sources add only 3 dB (not double) because intensity doubles. 60 dB + 60 dB = 63 dB. 70 dB + 60 dB ≈ 70.4 dB (louder one dominates).

Combining Sound Levels L_total = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10) + … + 10^(Lₙ/10)) This converts each source back to intensity (relative), sums them, then converts back to dB.

Quick Rules Same level, 2 sources: L_total = L + 3 dB Same level, 4 sources: L_total = L + 6 dB Same level, 10 sources: L_total = L + 10 dB Difference ≥ 10 dB: louder source dominates (+ 0.4 dB or less) Difference 5 dB: combined = louder + 1.2 dB Difference 3 dB: combined = louder + 1.8 dB Difference 0 dB: combined = louder + 3 dB

dB Reference Values dB SPL (sound pressure level): reference 20 μPa (threshold of hearing) dB SIL (intensity): reference 10⁻¹² W/m² L_p = 20 × log₁₀(p / p_ref) for a pressure ratio L_I = 10 × log₁₀(I / I_ref) for an intensity ratio

Common Sound Levels (dB SPL) Threshold of hearing: 0 dB | Whisper: 30 dB Conversation: 60 dB | Busy street traffic: 70 dB Lawnmower: 90 dB | Concert: 110 dB Jet engine at 30 m: 140 dB | Pain threshold: 130–140 dB

The practical consequence people get wrong

Noise control budgets get spent on the wrong machine constantly, and the arithmetic above is why. Say a workshop has a dust extractor at 92 dB and a compressor at 80 dB. The compressor is the one everyone complains about because it cycles on and off, so it gets the enclosure. Combined, the pair measure 92.3 dB. Box in the compressor and you are left with 92 dB, a change of three tenths of a decibel that no ear on earth can detect. The money bought nothing.

Deal with the extractor instead and the room drops to 80 dB, which is the difference between needing hearing protection and not. The rule that falls out of it: find the loudest source and start there, and only move on to the next once the gap between them has closed to within about 5 dB.

The same logic runs backwards for machine buyers. Adding a second unit identical to one you already have costs 3 dB. Adding a tenth costs 10 dB over the single machine, not ten times anything. Noise grows slowly with headcount, which is exactly why a busy plant room can sound only moderately worse than a quiet one.