Decibel Addition Calculator (Multiple Sources)

Because 3 dB IS a doubling — of energy: the decibel scale compresses each ×10 of power into +10 dB, so ×2 becomes 10·log₂ ≈ 3.01 dB. Two dishwashers, two lanes of traffic, two fan arrays: each doubling of identical incoherent sources steps the level by 3. The subjective twist: humans judge '+10 dB' as roughly 'twice as loud' — so DOUBLING the machinery (+3 dB) sounds like a 23% loudness increase, and making something 'sound half as loud' requires removing 90% of the acoustic energy.

The 10-dB rule: a source 10 dB below the dominant one raises the total by just 0.4 dB — inaudible in practice; at 6 dB down it adds 1.0 dB, at 3 dB down 1.8 dB. The noise-control corollary is brutal and money-saving: treating ANY source other than the loudest is nearly pointless until they're within a few dB of each other. Silence the 95-dB compressor before spending a rupee on the 85-dB fan beside it — this calculator's 'above the loudest' output is that priority list.

Incoherent = unrelated waveforms (different machines, traffic, crowd noise) — their phases are random, so powers add. COHERENT sources (the same signal from two speakers) add as amplitudes with phase: up to +6 dB where waves align, total cancellation where they oppose — the physics of subwoofer placement, line arrays and noise-cancelling headphones. Real-world mixed cases (two speakers playing different music: incoherent; the same track: coherent at low frequencies, messier above) are why PA alignment is a profession. This tool assumes incoherence — correct for noise sources, conservative for synced speakers.

Same energy logic in reverse: L_source = 10·log₁₀(10^(L_total/10) − 10^(L_background/10)). Measure with the machine on (total), then off (background); if they differ by 10+ dB, the correction is negligible; at 6 dB subtract ~1.3; at 3 dB subtract 3 — and below 3 dB difference the measurement is unreliable (the machine is quieter than the uncertainty). Occupational-hygiene standards build exactly these correction tables; the formula above is where they come from.