Sound Intensity Calculator | dB
Calculate sound intensity level in dB from intensity, and convert between intensity and dB.
Common sound sources:
INVERSE SQUARE LAW, Distance Effect (optional)
Every doubling of distance → −6 dB decrease
What Is the Sound Intensity Calculator | dB?
The Sound Intensity Calculator converts between sound level in decibels (dB SPL) and physical intensity in watts per square metre (W/m²), using the standard reference intensity I₀ = 10⁻¹² W/m² (the threshold of human hearing at 1 kHz). An optional inverse square law section calculates how sound level changes with distance from the source. A colour-coded dB gauge provides immediate visual context for where the level falls on the safe/dangerous hearing spectrum.
- ›dB formula: L = 10 × log₁₀(I/I₀), logarithmic scale matches human auditory perception
- ›Every 10 dB increase: 10× higher intensity (sounds about 2× louder to human ears)
- ›Every 6 dB increase: approximately double the sound pressure level
- ›Inverse square law: intensity drops to 1/4 each time distance doubles (−6 dB)
Formula
Sound Intensity Formulas
dB formula
L = 10 × log₁₀(I / I₀)
Intensity
I = I₀ × 10^(L/10)
Reference I₀
I₀ = 10⁻¹² W/m² (threshold)
Inverse sq.
I ∝ 1/r² (point source)
Distance dB
ΔL = −20 × log₁₀(r₂/r₁)
Double dist.
ΔL = −6 dB per doubling
How to Use
- 1Select mode: "dB → Intensity (W/m²)" or "Intensity → dB"
- 2Enter the sound level in dB, or the intensity in W/m² (use scientific notation like 1e-6)
- 3Click a common sound source button to auto-fill a known dB value
- 4Optionally enter reference and new distances for an inverse square law calculation
- 5Click Convert, the dB gauge colour-codes the result: green (safe), amber (caution), red (dangerous)
- 6Step-by-step working shows each calculation stage
Example Calculation
Normal speech at 60 dB → intensity:
I = 10⁻¹² × 10^(60/10)
I = 10⁻¹² × 10⁶
I = 10⁻⁶ W/m²
Moving from 1 m to 4 m from a source at 80 dB:
ΔL = −20 × log₁₀(4) = −20 × 0.602 = −12.04 dB
New level = 80 − 12.04 = 67.96 dB
OSHA hearing damage guidelines
OSHA permissible noise exposure: 90 dB for 8 hours. Each 5 dB increase halves the permissible duration: 95 dB for 4 hours, 100 dB for 2 hours, 115 dB for 15 minutes. Rock concerts (110–120 dB) can cause permanent hearing loss within minutes of unprotected exposure.
Understanding Sound Intensity | dB
Common Sound Levels Reference
| Source | dB Level | Intensity (W/m²) | Health note |
|---|---|---|---|
| Threshold of hearing | 0 dB | 10⁻¹² W/m² | Barely audible 1 kHz |
| Whisper at 1 m | 30 dB | 10⁻⁹ W/m² | Very quiet |
| Normal conversation | 60 dB | 10⁻⁶ W/m² | Safe indefinitely |
| Busy restaurant | 70 dB | 10⁻⁵ W/m² | Safe for 8+ hours |
| Vacuum cleaner | 80 dB | 10⁻⁴ W/m² | OSHA monitoring begins at 85 |
| Power tools | 100 dB | 10⁻² W/m² | 2 hour OSHA limit |
| Rock concert | 110 dB | 10⁻¹ W/m² | 30 min NIOSH limit |
| Threshold of pain | 130 dB | 10 W/m² | Immediate risk |
| Jet engine at 30 m | 140 dB | 100 W/m² | Eardrum rupture risk |
Frequently Asked Questions
What is the decibel scale?
The logarithmic dB scale compresses the enormous range of sound intensities (10¹⁴-to-1 from threshold to pain) into a manageable 0–140 scale that corresponds to subjective loudness.
- ›0 dB: threshold of hearing, I = 10⁻¹² W/m² (barely audible 1 kHz tone)
- ›60 dB: normal speech, I = 10⁻⁶ W/m² (1,000,000× reference)
- ›120 dB: threshold of pain, I = 1 W/m² (10¹² × reference)
- ›140 dB: jet engine, I = 100 W/m², eardrum rupture risk
How much louder is 10 dB?
The disconnect between intensity and perceived loudness is fundamental to acoustics. Intensity is a physical measurement; loudness is a perceptual one, measured in phons or sones.
- ›+3 dB: ~2× more intense, slightly noticeable difference
- ›+6 dB: ~4× more intense, clearly louder
- ›+10 dB: 10× more intense, sounds ~2× as loud to human ears
- ›+20 dB: 100× more intense, sounds ~4× as loud
What is the inverse square law for sound?
The inverse square law follows from geometry: sound radiates as an expanding sphere, so the same power is spread over an area 4πr², four times larger when r doubles.
- ›1 m → 2 m: −6 dB (intensity × 0.25)
- ›1 m → 10 m: −20 dB (intensity × 0.01)
- ›1 m → 100 m: −40 dB (intensity × 0.0001)
- ›Applies to free-field outdoors; indoors, reflections add reverberant field
At what dB level is hearing damage a risk?
Noise-induced hearing loss is cumulative and permanent, the hair cells in the cochlea that are damaged do not regenerate. Early hearing loss often starts at high frequencies (4 kHz notch).
- ›85 dB: OSHA action level, employer must offer hearing protection
- ›90 dB: OSHA PEL for 8 hours (many health agencies recommend 85 dB limit)
- ›110 dB: rock concert, damage within 2 minutes unprotected
- ›Most effective protection: distance + earplugs (30 dB attenuation) + duration limits
How are sound pressure level (SPL) and intensity different?
In practice, SPL meters measure pressure (easier to measure with a microphone), while intensity probes (two microphones) measure intensity directly. For plane waves in air, the two dB values are approximately equal.
- ›Reference pressure: p₀ = 20 μPa (corresponds to I₀ = 10⁻¹² W/m²)
- ›SPL formula: L_p = 20 × log₁₀(p/p₀) [note: factor 20, not 10]
- ›Intensity: L_I = 10 × log₁₀(I/I₀) [factor 10]
- ›Factor difference (10 vs 20): because I ∝ p², so dB(I) = 2×dB(p) with factor 10 = factor 20
How do you add decibel levels from two sources?
Sound sources add on an intensity (power) basis, not a dB basis. This is because dB is a logarithmic scale, you must convert to the linear domain first.
- ›Two sources at 70 dB: I_total = 2 × 10⁻⁵ W/m² → L = 73 dB (not 140!)
- ›Two equal sources: always +3 dB regardless of level
- ›Adding a source 10 dB quieter than the main: total ≈ main + 0.4 dB (negligible)
- ›Rule of thumb: 6 dB louder source dominates; 10 dB louder completely masks
What is the difference between dB SPL, dBA, and dBC?
The human ear is not equally sensitive at all frequencies. Weighting curves adjust the measured level to approximate perceived loudness, making dBA more meaningful than raw dB for noise health assessments.
- ›dBA: most common for noise regulations (OSHA, EPA, WHO use dBA)
- ›A-weighting: reduces below 1 kHz and above 6 kHz by 10–40 dB
- ›Midrange (1–4 kHz): A-weighted ≈ dB SPL (ear most sensitive here)
- ›dBC: used for peak measurements (gunshots, explosions) and music playback specs