Sound Intensity Level Calculator
Enter sound intensity I to get the level in decibels β=10·log₁₀(I/I₀), with I₀=10⁻¹² W/m². Whisper 1e-10 → 20 dB; conversation 1e-6 → 60 dB; rock concert 1 → 120 dB.
Input Data
Results
At a glance:Sound intensity level (SIL) quantifies sound energy flow density on a logarithmic decibel (dB) scale. The ear copes with intensities from 10⁻¹² W/m² up to 1 W/m² — a span of 12 orders of magnitude (10¹²×) — so a linear scale is impractical; the dB scale compresses it: +10 dB means intensity ×10, −10 dB means ÷10 (so +3 dB ≈ ×2, −3 dB ≈ ÷2). The formula is β=10·log₁₀(I/I₀), with reference I₀=10⁻¹² W/m² (the average threshold of hearing for a 1 kHz pure tone). Example: a library at I=10⁻⁸ W/m² gives β=10·log₁₀(10⁻⁸/10⁻¹²)=10·log₁₀(10⁴)=40 dB; normal conversation 1 m (I=10⁻⁶) → 60 dB; a rock concert front row (I=1) → 120 dB (pain threshold); a jet at 30 m (I=10⁴) → 160 dB (instant ear damage). In a plane or spherical free field the sound pressure level L_p ≈ sound intensity level L_I, so SPL is shown as an approximation. Properties: (1) dB is a ratio of powers, not a linear quantity; (2) adding two equal sources raises the level by 3 dB, not 6; (3) prolonged exposure above 85 dB risks hearing loss — use ear protection. Applications: (1) occupational noise limits and hearing protection; (2) room and concert-hall acoustics; (3) audio mixing and microphone gain; (4) environmental noise ordinances (Hong Kong limits construction noise); (5) DSE Physics.
Formula
Sound intensity level: β = 10·log₁₀(I/I₀) (dB)
Reference: I₀ = 10⁻¹² W/m² (threshold of hearing)
+10 dB → intensity ×10; +3 dB ≈ ×2; −10 dB → ÷10
Free field: SPL ≈ SIL
$$L_I = 10\log_{10}\left(\frac{I}{I_0}\right), \quad I_0 = 10^{-12}\ \mathrm{W/m^2}$$How to Use
- Enter sound intensity I (W/m²; scientific notation like 1e-6 allowed).
- The tool shows level β (dB), ratio I/I₀ and approximate SPL.
- Use a positive I; I≤0 returns 0 to avoid log errors.
Case Studies
Everyday sound levels
Breathing / leaf rustle 1e-11 → 10 dB (very quiet).
Library 1e-8 → 40 dB; office 1e-7 → 50 dB.
Conversation 1 m 1e-6 → 60 dB; vacuum 1e-4 → 80 dB; rock front 1 → 120 dB.
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.