Distance Attenuation Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Sep 08, 2022

This distance attenuation calculator is a tool that lets you analyze how the sound propagates in the air. The further away you are from the sound source, the lower the perceived sound intensity. We can describe the exact relationship between the sound level and distance using the sound attenuation formula.

In this article, we will show you how to calculate the exact sound level at any distance from the source. We will also provide you with a rule of thumb to quickly estimate the drop in volume – without using any calculations whatsoever!

What is the SPL (sound pressure level)?

All sounds we hear are nothing but vibrations traveling through the air (or other mediums). These vibrations exert a certain pressure on our ears.

One of the ways to measure this sound pressure is using regular units of pressure, called pascals. This approach is hugely inconvenient. Why? The quietest sounds we can hear – our hearing threshold – is about 0.00002 Pa. Expressing sound levels in fractions of a thousandth of a pascal is all but intuitive.

That is why, instead of regular pressure units, we use dedicated sound pressure units called decibels. The decibel (dB) scale is logarithmic, meaning that an increase of roughly 3 dB is equivalent to doubling the pressure, expressed in Pascals.

When SPL is given in decibels, we can estimate the pressure of everyday sounds, usually in the 20-100 dB range. 120 or 130 dB is the pain threshold – for example, a jet aircraft taking off in your immediate neighborhood will emit this level of sound.

Sound attenuation formula

Sound attenuation describes how the SPL changes with increasing distance from the sound source. For example, you can imagine two houses standing close to a highway. If you measure the distance from each of the buildings to the road and the SPL of one of them, you will be able to calculate the sound level in the other house.

The sound attenuation formula is as follows:

SPL2=SPL120log(R2R1)\small \text{SPL}_2 = \text{SPL}_1 - 20\log\left(\frac{R_2}{R_1}\right)

where:

  • SPL1\text{SPL}_1 – Sound pressure level at point 1;
  • SPL2\text{SPL}_2 – Sound pressure level at point 2;
  • R1R_1 – Distance from the sound source to point 1; and
  • R2R_2 – Distance from the sound source to point 2.

Inverse square law

Now, imagine that the distance from the sound source to point 1 is two times smaller than the distance from the source to point 2. In other words, R1=0.5×R2R_1 = 0.5 \times R_2. In this case:

SPL2=SPL120log ⁣(R2R1)=SPL120log ⁣(R20.5×R2)=SPL120log(2)=SPL120×0.301=SPL16.02 dB\small \begin{align*} \text{SPL}_2 &= \text{SPL}_1 - 20\log\!\left(\frac{R_2}{R_1}\right)\\[1em] &= \text{SPL}_1 - 20\log\!\left(\frac{R_2}{0.5 \times R_2}\right)\\[1em] &= \text{SPL}_1 - 20\log(2)\\[1em] &= \text{SPL}_1 - 20\times 0.301\\[1em] &= \text{SPL}_1 - 6.02\ \text{dB} \end{align*}

We have just calculated that when the distance from the sound source is two times smaller, the sound pressure level increases by 6 dB. What does it mean?

Hopefully, you remember that an increase of 3 dB means a doubling of the sound pressure. Following that logic, a gain of 6 dB is actually a fourfold increase in SPL. Each time you reduce the distance to the source by a factor of 2, the SPL increases by a factor of 4.

This rule is known as the inverse square law. You can use it to roughly estimate the change in SPL without actually doing any real calculations. If you need exact numbers, though, don't hesitate to use this distance attenuation calculator!

FAQ

How do I calculate the sound pressure level change with distance?

To calculate SPL change between two points, follow these steps:

  1. Measure the distances: from the sound source to points 1 and 2. Let's Denote them by R1 and R2.
  2. Compute the ratio R2/R1.
  3. Take log and multiply the result by 20.
  4. What you got is the SPL difference between the two points in question.

What is the 3 dB rule?

The 3 dB rule states that if you double the power, you gain roughly 3 dB. Conversely, halving the power implies a loss of approximately 3 dB.

What is the 6 dB rule?

The 6 dB rule states that whenever the distance that separates you from the sound source doubles (e.g., you move from 100 to 200 feet away from the source), the sound decreases by 6 dB. Equivalently, SPL decreases by a factor of 4.

How much louder is 40 dB than 20 dB?

40 dB is 100 times louder than 20 dB. Similarly, 80 dB is 100 times louder than 60 dB. This is because the decibel scale is logarithmic, and an increase of 10 dB corresponds to ten times more power.

Bogna Szyk
Point 1
Distance from the source
ft
Sound pressure level
dB
Point 2
Distance from the source
ft
Sound pressure level
dB
Sound level difference
Difference in SPL
dB
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