Distance Attenuation Calculator

What Is Distance Attenuation?

Distance attenuation describes how wave intensity decreases as it spreads outward from a source. Sound, light, and radio signals all follow the inverse square law in free space: doubling the distance reduces intensity to one quarter of its original value.

Inverse Square Law Formula

$$I_2 = I_1 \left(\frac{d_1}{d_2}\right)^2$$

where $I_1$ is intensity at reference distance $d_1$, and $I_2$ is intensity at the new distance $d_2$. If you move from 1 m to 2 m, intensity drops to 25% of the original.

Decibel Loss

$$\Delta \text{dB} = 10 \log_{10}\left(\frac{I_1}{I_2}\right) = 20 \log_{10}\left(\frac{d_2}{d_1}\right)$$

Doubling distance causes a 6.02 dB loss. This formula applies to point sources in an open medium without reflections or absorption.

Related tools: Sound Intensity Decibels Calculator.

Frequently Asked Questions

Why does intensity fall with the square of distance?

Energy spreads over a spherical surface area that grows as 4πr². The same total power is distributed over a larger area, so intensity per unit area decreases as 1/r².

Does this apply to sound and light?

Yes, in ideal conditions. Both follow the inverse square law for point sources. Real environments add absorption, reflection, and diffraction effects.

How many decibels are lost when distance doubles?

Exactly 6.02 dB. Each doubling of distance adds another 6.02 dB of attenuation.

What if the new distance is closer than the reference?

Intensity increases. Moving from 2 m to 1 m quadruples intensity, a gain of 6.02 dB (shown as negative loss).

Does atmospheric absorption affect this?

Yes. The inverse square law is geometric spreading only. Air, water, and obstacles cause additional attenuation beyond distance alone.

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What Is Distance Attenuation?

Inverse Square Law Formula

Decibel Loss

Frequently Asked Questions

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