Sound Energy Calculator
Convert between sound pressure level (SPL) and sound power in watts. Handles both free-field (4πr²) and hemi-anechoic (2πr²) radiation per ISO 3741/3744, with reference comparisons from breathing (10 dB) up to jet engines (140 dB+).
Input
Result
SPL & Intensity at Common Distances
| Distance | SPL | Intensity |
|---|
Real-World SPL & Power Reference
| Source | Typical SPL | Approx. sound power |
|---|---|---|
| Threshold of hearing (1 kHz) | 0 dB | ~10⁻¹² W (1 pW) |
| Breathing | 10 dB | ~10⁻¹¹ W |
| Rustling leaves | 20 dB | ~10⁻¹⁰ W |
| Whisper (1 m) | 30 dB | ~10⁻⁹ W (1 nW) |
| Library / quiet office | 40 dB | ~10⁻⁸ W |
| Refrigerator hum | 50 dB | ~10⁻⁷ W |
| Normal conversation (1 m) | 60 dB | ~10⁻⁶ W (1 µW) |
| Vacuum cleaner | 70 dB | ~10⁻⁵ W |
| City traffic / loud restaurant | 80 dB | ~10⁻⁴ W |
| Lawn mower / shouting | 90 dB | ~10⁻³ W (1 mW) |
| Jackhammer (1 m) | 100 dB | ~10⁻² W |
| Rock concert / chainsaw | 110 dB | ~10⁻¹ W |
| Jet takeoff (30 m) | 120 dB | ~1 W |
| Pain threshold | 130 dB | ~10 W |
| Gunshot / fireworks (close) | 140 dB | ~100 W |
| Jet engine / rocket (very close) | 150–180 dB | ~1 kW – 1 MW |
Power values are rough order-of-magnitude estimates for free-field radiation at the listed reference distance.
About Sound Energy
Sound is energy in motion. A vibrating source radiates acoustic power (measured in watts) into the surrounding medium. As the wavefront expands, that fixed power is spread over a larger and larger surface area, so the intensity (power per unit area, W/m²) drops with distance. This calculator handles the chain: SPL ↔ intensity ↔ power, with explicit handling of distance and radiation geometry.
SPL (sound pressure level)
What microphones and ears actually measure — a logarithmic ratio of pressure perturbation: SPL = 20·log₁₀(p / p_ref) where p_ref = 20 µPa (threshold of hearing in air). Equivalent intensity formula: SPL = 10·log₁₀(I / I_ref) with I_ref = 1 pW/m². SPL is what's quoted on noise data sheets and what OSHA regulates.
Sound power (P) and sound power level (Lw)
The source property — independent of where you stand to measure. A given speaker driver radiating 1 W into a room produces 1 W whether you're 1 m or 10 m away (the SPL changes, the power doesn't). Lw is the dB form: Lw = 10·log₁₀(P / P_ref) with P_ref = 1 pW. Manufacturers spec speakers in Lw because it's location-independent and adds simply.
Free field vs hemi-anechoic radiation
Free-field radiation assumes the source sits in unbounded space — power spreads over a full sphere of area 4πr². Hemi-anechoic radiation models a source on a rigid floor — power spreads over a hemisphere of area 2πr², doubling the intensity at the same distance (+3 dB). ISO 3744 specifies hemi-anechoic measurement (test source on a hard floor in an anechoic room). Real environments are somewhere in between; rooms add reverberation, raising SPL above the free-field prediction.
Inverse-square law
Doubling the distance reduces SPL by exactly 6 dB in free field — intensity drops to 1/4 because area grew 4×. So if 80 dB at 1 m, then 74 dB at 2 m, 68 dB at 4 m, 62 dB at 8 m, and so on. This is why personal listening volume drops dramatically with distance from a speaker, and why concert sound systems use distributed line-arrays to fight the loss.
Frequently Asked Questions
Why is 80 dB SPL only about 1 milliwatt of power?
Why does the SPL drop by exactly 6 dB per doubling of distance?
What's the difference between SPL (dB) and Lw (dB)?
I_ref = 1 pW/m² — a power per area, so it depends on where you measure. Lw uses P_ref = 1 pW — total radiated power, no distance involved. They're numerically equal only when the measurement sphere area equals exactly 1 m² (a sphere of radius r = 1/(2√π) ≈ 0.282 m). For other distances, SPL = Lw − 10·log₁₀(4πr²) = Lw − 10·log₁₀(area).When should I use free field vs hemi-anechoic?
How do I add two sound sources?
SPL_sum = 10·log₁₀(10^(SPL₁/10) + 10^(SPL₂/10)). See the dB Addition Calculator.Why is the threshold of hearing exactly 0 dB SPL?
p_ref = 20 µPa was chosen as the reference pressure to make the threshold of hearing at 1 kHz come out to 0 dB. Below 0 dB SPL is audible only to people with exceptional hearing or in very rare environments (sub-zero dB SPL has been measured in anechoic chambers). Above ~120 dB SPL is the threshold of physical pain. The 0-120 dB range spans 12 orders of magnitude of intensity — which is why we use the logarithmic dB scale.