Decibel Distance Calculator
Sound level at any distance from a known reading, by inverse square law.
What it does
Sound thins as it spreads. From a small source outdoors, acoustic energy crosses ever larger spheres, so intensity falls with the square of distance. On the decibel scale that geometry becomes a straight rule: every doubling costs about 6 dB.
The tool above applies L2 = L1 - 20 x log10(r2/r1) the moment you type. Enter a known level with its distance, then the target distance. It returns the new level, the change, and the doubling count. Defaults of 90 dB at 10 ft to 40 ft open solved at 78 dB.
The 20 in the formula is doing the physics. Intensity ratios use 10 x log10, but pressure ratios square first, doubling the factor to 20. A distance ratio of 4 gives 20 x 0.602 = 12 dB, exactly two doublings at 6 each, which is how the worked case cross checks.
Real sites deviate because the law assumes a free field: no ground bounce, walls, wind gradients, or barriers. Hard ground adds a few dB back, soft grass and wind shadows subtract more, and rooms replace the rule with reverberation math entirely. Read the page as the outdoor baseline, then measure.
Use the table to lock in the doubling ladder, then run the machine. When the answer nears 85 dBA at a worker position, protection and exposure math take over from geometry.
How to use
- Pick imperial (ft) or metric (m).
- Enter the known level and its distance.
- Enter the distance to predict.
- Read the new level first, then the change.
- Count doublings to sanity check 6 dB each.
- Measure on site when compliance is at stake.
Formula
- L1
- Level at the reference distance, in dB.
- r1
- Reference distance: ft imperial, m metric.
- r2
- Second distance in the same unit.
Free field point source with no reflections, in dB. Each doubling of distance costs about 6 dB because 20 x log10(2) = 6.02. Distances share one unit per calculation: feet in imperial mode, meters in metric.
Worked example
Example: 90 dB at 10 ft, heard at 40 ft
A machine reads 90 dB at 10 ft. Find the level at 40 ft in a free field.
- Write the law: L2 = L1 - 20 x log10(r2 / r1).
- Ratio: 40 / 10 = 4.
- Loss: 20 x log10(4) = 20 x 0.602 = 12 dB.
- Level: 90 - 12 = 78 dB.
- Doublings: log2(4) = 2, at 6 dB each gives 12 dB back.
- Metric mirror: 90 dB at 3 m reads 78 dB at 12 m.
Reference table
| Distance | Ratio | Level |
|---|---|---|
| 10 ft (reference) | 1 | 90 dB |
| 20 ft | 2 | 84 dB |
| 40 ft (worked case) | 4 | 78 dB |
| 80 ft | 8 | 71.9 dB |
| 25 ft from 80 dB at 50 ft | 0.5 | 86 dB |
Limits
- Free field point source only; rooms differ.
- No wind, ground, or barrier effects.
- A weighted hearing risk needs dBA plus time.
- Two sources need energy addition, not this page.
Common mistakes
- Subtracting distances instead of taking the log ratio.
- Mixing feet with meters in one calculation.
- Applying point rules to road line sources.
- Expecting indoor rooms to follow 6 dB.
- Adding two decibel values arithmetically.
Try it yourself
Quick checks. Answers sit tucked under each question.
80 dB at 50 ft, heard at 25 ft?
Closer doubles once in reverse: 80 + 6 = 86 dB, change -6 dB, -1 doublings.
100 dB at 5 ft, heard at 20 ft?
Ratio 20 / 5 = 4, loss 12 dB, so 100 - 12 = 88 dB with 2 doublings.
Why does the metric default match?
3 m to 12 m is also a ratio of 4, so the same 12 dB loss: 78 dB.
Questions
What is the doubling rule?
6 dB per doubling for a point source in a free field. Double 10 to 20 ft and 90 becomes 84.
Do roads fade the same way?
Line sources like roads spread cylindrically and fall about 3 dB per doubling. This page covers point sources only.
Why does my meter disagree?
Wind, ground, barriers, and reflections bend real readings several dB either way. Treat the page as a free field baseline.
What level is legally safe?
OSHA uses 90 dBA for 8 hours with a 5 dB exchange rate, while NIOSH recommends 85 with 3 dB. Both sit below the physics here.
Can I add two machines with this page?
Decibels add by energy, not arithmetic: 90 plus 90 is 93, not 180. The companion addition page handles that.
What about moving closer?
Yes. Below the reference distance the log term goes negative and the level rises: 80 dB at 50 ft reads 86 at 25.
Sources
- OSHA Technical Manual: noise, inverse square law and 6 dB rule
- AIHA: sound pressure level between two points (inverse square formula)