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.

Solve for

Acoustic power P (W)

Distance r (m)

Target intensity (W/m²) - for distance or power mode

3.18e-3 W/m²

sound intensity at 5 m

Sound level95.03 dB

Sphere area at r314.16 m²

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.

Frequently asked questions

What is the inverse square law for sound?

The inverse square law states that sound intensity is inversely proportional to the square of the distance from the source. The formula is I = P divided by (4 pi r squared), where P is the acoustic power in watts and r is the distance in metres. Doubling the distance from a point source reduces the intensity to one quarter of its previous value, which is a drop of about 6 dB.

How do you convert sound intensity to decibels?

Sound intensity level in decibels is L = 10 times log base 10 of (I divided by I0), where I0 is the reference intensity of 1 times 10 to the power of negative 12 watts per square metre. For example, an intensity of 1 times 10 to the power of negative 3 W/m squared gives L = 10 times log10(1e-3 divided by 1e-12) = 10 times 9 = 90 dB.

What is a point source assumption for sound?

The inverse square law assumes a point source radiating uniformly in all directions into free space with no reflections. Real sources are not perfect points, and reflections from walls or surfaces can add to the measured intensity. The formula gives a useful first estimate of intensity outdoors away from boundaries.

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