Loudspeaker coverage
Inverse Square Law Chart
Quick answer
Doubling the distance from a loudspeaker costs exactly 6.02 dB in a free field, so a seat at 80 feet is 18 dB quieter than one at 10 feet. In a real sanctuary the loss stops at the critical distance, beyond which reflected energy holds the level up but destroys clarity.
The inverse square law is the reason the front row complains that the system is too loud while the back row cannot hear the words. Sound radiating from a point source spreads over the surface of an expanding sphere, so the energy per unit area falls with the square of the distance. In decibels that is a clean and memorable rule: change = -20 log10(d2 / d1), which makes every doubling of distance cost 6.02 dB.
This single relationship drives loudspeaker placement, delay fill design, and the whole argument for line arrays in deep rooms. It is also the rule most often misapplied, because a sanctuary is not a free field. Work your own seats with the SPL loss by distance calculator.
On this page
How much level is lost at each distance?
Referenced to a listener 10 feet from the loudspeaker. Each row is the level change relative to that reference, and the last two columns show what it means for a system set to a comfortable level near the front.
Every doubling of distance costs 6.02 dB, so a seat 80 feet from the loudspeaker receives 18.1 dB less than a seat at 10 feet.
| Distance | Change from 10 ft | A 95 dBA front position becomes | Doublings from 10 ft |
|---|---|---|---|
| 10 ft | 0.0 dB | 95.0 dBA | Reference |
| 14 ft | -2.9 dB | 92.1 dBA | Half a doubling |
| 20 ft | -6.0 dB | 89.0 dBA | 1 |
| 28 ft | -8.9 dB | 86.1 dBA | 1.5 |
| 40 ft | -12.0 dB | 83.0 dBA | 2 |
| 56 ft | -15.0 dB | 80.0 dBA | 2.5 |
| 80 ft | -18.1 dB | 76.9 dBA | 3 |
| 113 ft | -21.1 dB | 73.9 dBA | 3.5 |
| 160 ft | -24.1 dB | 70.9 dBA | 4 |
Free field means no reflecting surfaces. Outdoors on grass this is close to the truth. Indoors it holds only until reflected energy becomes comparable to direct energy, which in a typical sanctuary is somewhere between fifteen and forty feet from the loudspeaker.
Actual sound level at each seat
Level produced by a single loudspeaker of 96 dB sensitivity, at one watt, one hundred watts and five hundred watts. This is the arithmetic that decides whether an amplifier is big enough for the back row.
A 96 dB sensitivity loudspeaker driven with 100 watts produces about 86.3 dBA at 100 feet and 106.3 dBA at 10 feet, which is the 20 dB the inverse square law predicts across that tenfold distance.
| Distance | At 1 watt | At 100 watts | At 500 watts |
|---|---|---|---|
| 3.3 ft (1 metre) | 96.0 dBA | 116.0 dBA | 123.0 dBA |
| 10 ft | 86.3 dBA | 106.3 dBA | 113.3 dBA |
| 20 ft | 80.3 dBA | 100.3 dBA | 107.3 dBA |
| 30 ft | 76.8 dBA | 96.8 dBA | 103.8 dBA |
| 40 ft | 74.3 dBA | 94.3 dBA | 101.3 dBA |
| 50 ft | 72.3 dBA | 92.3 dBA | 99.3 dBA |
| 60 ft | 70.8 dBA | 90.8 dBA | 97.7 dBA |
| 80 ft | 68.3 dBA | 88.3 dBA | 95.2 dBA |
| 100 ft | 66.3 dBA | 86.3 dBA | 93.3 dBA |
| 120 ft | 64.7 dBA | 84.7 dBA | 91.7 dBA |
Each tenfold increase in power adds 10 dB, and each doubling of distance subtracts 6 dB. Note that 100 watts at 100 feet gives 86.3 dBA, which is a perfectly adequate blended service level, and that reaching the same level at 120 feet takes more than 150 watts.
Where the rule stops being true
Inside a building, direct sound from the loudspeaker and reflected sound from the room arrive together. Direct sound obeys the inverse square law. Reflected sound is roughly constant throughout the room, because it has bounced so many times that it no longer has a direction. The distance at which the two are equal is called the critical distance, and it is the point where this chart stops describing reality.
Beyond the critical distance, adding level does not improve intelligibility, because the direct and reflected energy rise together and the ratio between them, which is what the ear uses to decode words, stays the same. This is the single most important acoustic fact in church sound and it explains a great deal:
- Why a reverberant stone sanctuary is loud at the back and still unintelligible.
- Why turning the system up makes a bad room worse rather than better.
- Why a narrow, well aimed loudspeaker outperforms a louder wide one, since it puts more direct and less reflected energy on the listener.
- Why delay fills work: they restore direct sound at a distant seat rather than adding more level from far away.
In a treated room with a short reverberation time, the critical distance is long and this chart is a decent guide throughout the seating. In an untreated stone or glass sanctuary it can be under fifteen feet, in which case almost every seat is in the reverberant field and the only real fix is absorption.
How to use the rule when placing loudspeakers
- Measure to the furthest seat the box will serve. From the loudspeaker itself, not from the front of the platform. This is the distance the amplifier is sized against.
- Work out the level difference across the seating. Compare the nearest and furthest seats the box covers. Anything above about 9 dB of variation will feel unbalanced.
- Fix the variation by aiming, not by level. Tilting the box so its on-axis line lands on the back row and the near seats sit off axis trades the inverse square loss against the coverage pattern, and can flatten the difference by several decibels for free.
- Add delay fills rather than more power for deep rooms. Past about 80 feet, a delayed fill restores direct sound locally. It needs a fraction of the power and it improves clarity rather than just level.
- Time align every fill. Delay equals the path difference in feet times 0.889 milliseconds, plus 10 to 15 milliseconds of Haas offset so the ear still localises the sound at the platform.
- Verify by walking the room during rehearsal. Meter at the front, middle and back of the seating with the same programme material and compare. The numbers tell you what to adjust.
Where this chart does not apply
It does not describe line arrays in their near field. A well designed line array behaves as a cylindrical rather than a spherical source over much of its range, which costs about 3 dB per doubling rather than 6. That halved loss is precisely why line arrays are used in deep rooms, and it makes every figure in these tables pessimistic for that case.
It does not apply below the critical distance boundary in a reverberant room. As above, most seats in an untreated sanctuary are in the reverberant field where level is roughly constant.
It ignores air absorption. Over long distances, high frequencies are absorbed by air itself, and the effect grows with distance, with frequency and with low humidity. Past about 100 feet this is audible as a loss of brightness that no amount of level restores, which is another argument for a delayed fill rather than a more powerful main system.
It assumes a point source. A large cabinet measured very close to itself does not behave as a point, which is why the standard measurement is taken at one metre and why comparisons at less than a few feet are meaningless.
It says nothing about directivity. A listener at 40 feet directly on axis and a listener at 40 feet at the edge of the coverage pattern both appear in the same row of this table and will hear very different things. Read this chart together with the coverage angle chart.
Sources
- Inverse square law and SPL at distance formulae as implemented in this site’s SPL and amplifier calculators
- Established room acoustics practice on critical distance and the direct to reverberant ratio
Frequently asked questions
How much sound level is lost per foot?
There is no fixed loss per foot, because the loss is proportional rather than linear. Doubling the distance always costs 6.02 dB, whether that is from 10 feet to 20 or from 60 feet to 120. Near the loudspeaker the loss per foot is steep, and far away it is very gradual, which is why the front rows are so much louder than everywhere else.
Why is my back row so much quieter than the front?
Geometry. A front seat at 15 feet and a back seat at 60 feet are two doublings apart, which is 12 dB, and 12 dB is a very large difference. Aiming the loudspeaker so its on-axis line lands on the back row while the front seats sit off axis recovers several decibels at no cost, and delayed fills recover the rest.
What is the critical distance?
The distance from a loudspeaker at which reflected energy in the room equals direct energy from the box. Closer than that, the inverse square law applies and clarity is good. Beyond it, level stops falling but intelligibility keeps degrading. In an untreated stone sanctuary it can be under fifteen feet, which means almost every seat is in the reverberant field.
Does turning the system up help the back row?
Only if the back row is inside the critical distance, which in most sanctuaries it is not. Beyond that point, raising the level raises direct and reflected energy equally, so the ratio the ear uses to decode speech does not improve. The back row gets louder mush. The real fixes are room absorption, tighter loudspeaker aiming and delayed fill speakers.
Why do line arrays lose less level with distance?
Because a long array behaves as a cylindrical source rather than a spherical one within its near field, so energy spreads over an expanding cylinder instead of an expanding sphere. That costs about 3 dB per doubling of distance rather than 6. Over a 100 foot room the difference accumulates to roughly 9 dB, which is why deep rooms use arrays.
How do I calculate the delay for a fill speaker?
Take the path difference in feet between the main loudspeaker and the fill for a listener sitting at the fill, multiply by 0.889 milliseconds per foot, then add 10 to 15 milliseconds of Haas offset. The offset is deliberate: arriving slightly late makes the ear localise the sound at the platform, so the fill speaker disappears rather than becoming its own source.
Researched, not professional advice. This page is compiled from published manufacturer specifications, operator manuals, FCC rules, published standards and owner-review consensus, not hands-on testing. Sound system design, rigging loudspeakers overhead, and any electrical work are jobs for a qualified professional: have flown loudspeakers and their attachment points signed off by a structural engineer or a certified rigger, and have all wiring done by a licensed electrician to your local code. Wireless microphone rules change, so confirm the current FCC position before buying. As an Amazon Associate we earn from qualifying purchases.