Sound Intensity Calculator
Sound intensity is the acoustic power passing through a unit area perpendicular to the direction of propagation. For a point source radiating equally in all directions into open space, the total power spreads over an ever-expanding sphere as the distance increases. Because the surface area of a sphere is 4 pi r squared, the intensity at distance r is I equals P divided by 4 pi r squared. This is the inverse square law: double the distance and the intensity drops to one quarter, which corresponds to a reduction of about 6 dB. This calculator applies that relationship in three modes. The first finds intensity and the decibel level from source power and distance. The second finds the distance at which a source of known power produces a target intensity. The third finds the source power required to produce a target intensity at a given distance. The reference intensity I0 equals 1 times 10 to the power of negative 12 watts per square metre, the standard threshold of hearing, is used throughout for the dB conversion. The calculator is used in environmental noise assessment, architectural acoustics, audio engineering, physics study, and speaker system design. Results assume an ideal point source in free field with no reflections or absorption. Real environments introduce reflections, scattering and absorption that will cause measured levels to differ from these predictions.
Assumes an ideal point source in free field (no reflections). Reference I₀ = 1 x 10⁻¹² W/m². Results are a theoretical estimate only.
How it works
The inverse square law gives intensity: I = P / (4πr²). The sphere surface area at distance r is A = 4πr². Sound level in decibels: L = 10 log₁₀(I / I₀). To find distance: r = sqrt(P / (4πI)). To find power: P = I x 4πr². Each doubling of distance reduces intensity by a factor of 4 (approximately 6 dB decrease).
Worked example
A speaker has an acoustic power of 1 W. At a distance of 5 m: sphere area = 4 x pi x 25 = 314.16 m². Intensity I = 1 divided by 314.16 = 3.18 x 10 to the power of negative 3 W/m². Sound level L = 10 x log₁₀(3.18e-3 divided by 1e-12) = 10 x log₁₀(3.18 x 10 to the power of 9) = 95.02 dB. These match the default values pre-filled above.
Related calculators
- Decibel Calculator: convert between intensity and dB, or combine two incoherent sources.
- Energy Converter: convert between joules, watts and other energy or power units.
- Percent Error Calculator: compare a measured sound level against a calculated prediction.
- Velocity Calculator: calculate the speed of sound or other waves.