Sound Energy Calculator
This sound energy calculator converts 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 outward as a spherical or hemispherical pressure wave, that fixed power is spread over a larger and larger surface area, so the sound intensity (power per unit area, W/m²) drops with distance. This calculator handles the full chain: SPL ↔ intensity ↔ acoustic power, with explicit handling of measurement distance and radiation geometry. It is the acoustic analogue of an electrical power calculator, but operating in the sub-milliwatt regime where decibels are essential for tractable notation.
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. The reverse operation — converting dB to watts — is what this calculator performs when you switch to "SPL → Power" mode. SPL is what's quoted on noise data sheets, equipment spec sheets, and what OSHA regulates. Note that OSHA and most noise ordinances cite A-weighted SPL (dB(A)) rather than flat unweighted SPL — A-weighting rolls off the low and high frequencies to model human hearing sensitivity. This calculator uses unweighted flat SPL; for A-weighted compliance checks, an integrating sound level meter (SLM) set to A-weighting is required.
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 spherical 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. Use the inverse square law calculator for quick SPL-vs-distance comparisons, or the dB addition calculator to correctly sum multiple independent sources.
dBFS vs dB SPL vs dBA — which decibels is this?
dBFS (decibels relative to digital full scale) is what an uncalibrated browser or phone microphone reports. It is always 0 or negative — 0 dBFS means the signal is at the maximum the analog-to-digital converter can record before clipping. It is a relative level with no fixed relationship to physical sound pressure; two phones held side by side in the same sound field will report different dBFS values depending on their microphone sensitivity and gain settings. dB SPL (sound pressure level) is an absolute physical scale referenced to 20 micropascals and requires a calibrated sound-level meter. dBA is A-weighted dB SPL — it applies a standardized filter that de-emphasizes low and very high frequencies to reflect how human hearing perceives loudness, and is the scale OSHA, NIOSH, and virtually all environmental noise regulations specify. This calculator works with calibrated dB SPL inputs; if you are copying readings from a phone app or browser-based microphone tool, those dBFS numbers are relative levels only, not certified dBA or SPL values. For noise-exposure compliance, use a calibrated sound-level meter set to A-weighting and slow time-averaging. See the noise exposure calculator for dose calculations and the sound pressure level calculator for SPL conversion details.
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.What is the difference between dB SPL and dB(A)?
What are the OSHA permissible noise exposure limits?
Does this calculator work in the near field of a source?
I = P / (factor · r²)) is only valid in the acoustic far field, where r is large compared to both the source dimensions and the acoustic wavelength. In the near field (very close to the source, typically r less than one wavelength or one source diameter), pressure does not follow the simple point-source model: reactive near-field pressure can exceed the far-field prediction, and the relationship between pressure and intensity is complex. As a rule of thumb, keep r at least a few source dimensions away, and at least one wavelength at the lowest frequency of interest. For a 100 Hz source (λ = 3.4 m), the far field begins around 3–5 m. Use the inverse square law calculator to quickly check SPL changes across distances once you are safely in the far field.