Calculate the missing sound level or distance from initial and final dB readings using the 20×log10 distance relationship and unit conversions for meters, feet, cm and inches.

Decibel Distance Formula

The following formula is used to estimate the distance between two points from the change in sound level (in dB) assuming free-field spherical spreading (no major reflections) and the same reference for both sound level readings.

D₂ = D₁ · 10^{((L₁ – L₂)/20)}

Where D₂ is the distance at point 2
D₁ is the distance at point 1
L₂ is the sound level at point 2 (dB)
L₁ is the sound level at point 1 (dB)

Because decibels are logarithmic, you can’t take a simple ratio of dB values. Instead, use the relationship between sound level change and distance: a change of 20·log₁₀(D₂/D₁) dB corresponds to a distance ratio of D₂/D₁.

Decibel Distance Definition

What is decibel distance? “Decibel distance” commonly refers to the distance at which a sound level (in dB) would be expected to occur, given a known sound level at a different distance, under an assumed spreading model (often free-field spherical spreading).

Example Problem

How to calculate decibel distance?

First, determine the sound level at point 1.
The sound level at point 1 in this example is found to be 20 dB.
Next, determine the distance from the source at point 1.
The distance from the sound source to point 1 is found to be 20 ft.
Next, determine the sound level at point 2.
The sound level at point 2 is found to be 3 dB.
Finally, calculate the distance to point 2 from the source.
The final distance is calculated to be D₂ = 20 × 10^((20 − 3)/20) = 141.59 ft.

About Decibel Distance

How does sound change with distance? In a free field (approximately spherical spreading from a point source), sound intensity follows an inverse-square law (∝ 1/r²), and sound pressure level (in dB) decreases by 20·log₁₀(r) — about 6 dB for each doubling of distance.

Decibel Distance Calculator