Decibel (dB) & Sound Level Calculator

Decibels and Sound Guide

The Decibel Scale

The decibel (dB) is a logarithmic unit. dB = 10 × log₁₀(I/I₀), where I₀ = 10⁻¹² W/m² (threshold of human hearing). Because it is logarithmic: +10 dB = 10× more power/intensity. +3 dB ≈ 2× more power. +6 dB ≈ 4× more power. Common levels: 0 dB (threshold of hearing), 30 dB (quiet bedroom), 60 dB (normal conversation), 85 dB (heavy traffic), 100 dB (nightclub), 120 dB (jet engine at 100m), 140 dB (threshold of pain).

Combining Sound Levels

Two identical sound sources at 90 dB together produce 93 dB — not 180 dB. This is the logarithmic addition: total = 10 × log₁₀(10^(dB1/10) + 10^(dB2/10)). Two levels equal produce 3 dB more. Two levels 10 dB apart: the combined level is essentially the louder one (within 0.4 dB). This is why adding a second violin to an orchestra makes very little difference to overall volume — the orchestra's background noise dominates.

Hearing Damage and Safe Exposure

The Health and Safety Executive (UK) sets noise action levels: 80 dBA: employers must provide hearing protection if requested. 85 dBA: employers must supply and workers must use hearing protection. 87 dBA: absolute limit at ear (cannot be exceeded even with protection). Safe daily exposure times (approximately): 85 dB = 8 hours, 88 dB = 4 hours, 91 dB = 2 hours, 94 dB = 1 hour, 100 dB = 15 minutes, 110 dB = 2 minutes. Noise-induced hearing loss is permanent and cumulative — concert-going, power

Inverse Square Law

Sound intensity decreases with the square of distance: if you double your distance from a source, intensity reduces by 6 dB. At 1m from a speaker at 100 dB: at 2m = 94 dB, at 4m = 88 dB, at 10m = 80 dB, at 100m = 60 dB. This is why standing back from speakers at events reduces hearing damage risk dramatically. The inverse square law applies to point sources in open spaces — indoors, reflections mean sound does not decrease as rapidly with distance.