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

dB
m
Real-world references

Result

Result
SPL at distance
Sound power P
Intensity I at distance
Lw (ref 1 pW)
Formulas
I = I_ref · 10^(SPL/10), I_ref = 1 pW/m² = 10⁻¹² W/m²
Free field: P = 4π·r²·I ; Hemi-anechoic: P = 2π·r²·I
SPL at distance r = 10·log₁₀(P / (factor · r² · I_ref))
Sound power level Lw = 10·log₁₀(P / P_ref), P_ref = 1 pW = 10⁻¹² W

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)
Breathing10 dB~10⁻¹¹ W
Rustling leaves20 dB~10⁻¹⁰ W
Whisper (1 m)30 dB~10⁻⁹ W (1 nW)
Library / quiet office40 dB~10⁻⁸ W
Refrigerator hum50 dB~10⁻⁷ W
Normal conversation (1 m)60 dB~10⁻⁶ W (1 µW)
Vacuum cleaner70 dB~10⁻⁵ W
City traffic / loud restaurant80 dB~10⁻⁴ W
Lawn mower / shouting90 dB~10⁻³ W (1 mW)
Jackhammer (1 m)100 dB~10⁻² W
Rock concert / chainsaw110 dB~10⁻¹ W
Jet takeoff (30 m)120 dB~1 W
Pain threshold130 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?
Sound is energetically tiny compared to our perception of it. 80 dB SPL is "loud" subjectively, but the intensity is only 10⁻⁴ W/m² — a ten-thousandth of a watt per square meter. Multiplied by a 1 m² hemisphere area, that's ~6.3 × 10⁻⁴ W or ~0.6 mW radiated from a 1-m-distant source. Even a "rock concert" at 110 dB is about 100 mW of acoustic power. Speakers are rated at hundreds of watts of electrical input but radiate only 1-2% as sound — efficiency under 5% is typical for moving-coil drivers.
Why does the SPL drop by exactly 6 dB per doubling of distance?
Sound from a point source spreads over a spherical surface of area 4πr². When you double r, the area becomes 4π(2r)² = 4 × 4πr², so intensity drops by a factor of 4. In dB: 10·log₁₀(1/4) = −6 dB. Exact for free-field point sources at any frequency; real sources deviate when r is small relative to the source dimensions (near field) or when boundaries reflect sound (room).
What's the difference between SPL (dB) and Lw (dB)?
Both are decibel values but referenced to different quantities. SPL uses 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?
Free field approximates an outdoor open-air source with no reflecting surfaces — birds in mid-air, jet aircraft in flight, sources mid-room far from walls. Hemi-anechoic approximates a source on a hard floor in an otherwise anechoic environment — the floor reflects everything upward, doubling the intensity above. ISO 3744 uses hemi-anechoic because most consumer products (washing machines, lawn mowers, fans) sit on the ground. Real rooms are neither — they add reverberation that further raises measured SPL, typically by 3-10 dB depending on room size and absorption.
How do I add two sound sources?
Add their powers, not their SPLs. Two equal 70-dB sources: each radiates ~3.18 µW, sum = 6.36 µW, which back-converts to 73 dB SPL (+3 dB, double power). Two sources with different SPLs need logarithmic addition: 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?
Because 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.