What it does
Sound gets quieter with distance for two reasons. It spreads out: from a small source (a point) the same energy covers a sphere that grows with the square of the distance, so the level falls by 6 dB every time the distance doubles. A long, busy road or a pipe is a line source and falls by only 3 dB per doubling, and very close to a big flat source it hardly falls at all. And the air absorbs sound, very little at low frequencies but a lot at high ones, depending on temperature and humidity.
This calculator does both, for one frequency or for a whole octave band spectrum with the A-weighted total in dB(A), and draws the level against distance. It also finds the distance where the level falls to a target, and has a small decibel adder for adding levels, averaging them and taking off the background.
How to use it
- Choose whether you have one level at one frequency or octave band levels (63 Hz to 8 kHz, unweighted).
- Type the level and the distance r₁ where it was measured, and the distance r₂ where you want to know it.
- Choose the source type. Add any other losses in dB (a wall, a barrier, ground effect) if you know them.
- Optionally type a level to reach: the page finds the distance where the sound has fallen to it.
- Set the air temperature, humidity and pressure, or switch air absorption off.
- In the Add, average or subtract box, type a list of levels and, if you have it, the background level on its own.
Worked example
The made-up example is a machine giving 90 dB at 1 m at 1 kHz, on a 20 °C day at 50 % humidity. At 100 m the page shows 49.5 dB: spreading from a point takes off 40.0 dB (twenty times the log of 100), and the air takes another 0.46 dB (4.66 dB per km at 1 kHz). The level falls to 45 dB at 163 m, against 178 m if the air absorbed nothing.
For a spectrum, choose octave band levels: the example bands of 80, 84, 86, 88, 87, 84, 80 and 74 dB from 63 Hz to 8 kHz make 91.3 dB(A). Measured at 10 m and carried to 500 m at 15 °C and 70 % humidity, they become 54.6 dB(A); the 8 kHz band loses over 40 dB to the air alone, which is why distant noise sounds dull.
In the adder, 85, 82 and 79 dB together make 87.4 dB, with an energy average of 82.7 dB. With a background of 70 dB, the sources on their own are 87.4 dB: the background makes almost no difference when it is more than 10 dB below.
Tips
- Measure r₁ far enough away that the source looks small (at least two or three times its size), or the 6 dB rule over-predicts the fall.
- Outdoors over hard ground, reflections add up to 3 dB; wind blowing towards you and temperature inversions at night can carry sound much further than this calculator says.
- Two equal sources are 3 dB louder than one; ten equal sources are 10 dB louder.
FAQ
Why is the A-weighted result different from the unweighted one? A-weighting follows how the ear hears quiet sounds and turns the low bands down a lot, so a rumble counts for less in dB(A).
Can I use this for planning permission or a legal limit? It is a free-field estimate for study and planning, not a substitute for professional judgement or a proper noise survey made to the method your local rules require.
Where the numbers come from
- Geometric spreading from point (20 lg r) and line (10 lg r) sources and energy addition of levels: standard acoustics.
- Atmospheric absorption: the pure-tone formula of ISO 9613-1:1993 (relaxation of oxygen and nitrogen), used as a formula only; no tables copied.
- A-weighting: the analytic expression of the A-weighting curve given in IEC 61672-1, used as a formula.
- Checked against an independent NumPy and SciPy implementation (including a SciPy root search for the distance). The example levels are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.