Speaker SPL Calculator
Speaker loudness at seat and watts for target SPL.
What it does
Loudness at the couch follows three numbers: speaker sensitivity plus power gain minus distance loss. An 88 dB speaker on 100 watts at 4 meters plays 95.96 dB, and hitting 95 needs 80.2 of those watts. Every doubling of distance costs 6.02 dB while tenfold power buys 10.
The tool above runs the free-field point-source form. Enter sensitivity, watts, seat meters, and a target, and it prints seat SPL, watts for target, and the doubled-distance level. Defaults show the 88 dB case; practice spans 90 and 85 dB rigs.
Acoustics references agree. HyperPhysics derives the inverse square law with 6 dB per doubling and 20 dB per tenfold distance, and AES sensitivity standards define the 1 W / 1 m reference behind datasheet figures. The combined SPL equation appears across university and industry derivations identically.
Rooms bend the free field upward. Walls, floors, and ceilings add reflections that lift real seats a few dB over these numbers, while outdoors and anechoic spaces track them closely. Use the math for power planning, then measure the room for truth.
How to use
- Enter speaker sensitivity in dB.
- Enter amplifier watts.
- Enter the seat distance in meters.
- Enter the target dB.
- Read seat SPL first, then watts needed.
- Expect rooms a few dB hotter.
Formula
- sens
- dB at 1 W and 1 m on axis, 50 to 120.
- watts
- Amplifier watts into the speaker.
- dist
- Seat distance in meters.
Point-source free-field form (HyperPhysics inverse square; AES sensitivity standards). Doubling distance costs 6.02 dB.
Worked example
Example: 88 dB, 100 W, 4 m
Defaults: 88 dB, 100 W, 4 m, 95 dB target.
- Inputs: 88 dB sensitivity, 100 W, 4 m seat, 95 dB target.
- Power: 10 x log10(100) = 20 dB.
- Distance: 20 x log10(4) = 12.04 dB.
- Seat: 88 + 20 minus 12.04 = 95.96 dB.
- Target watts: 10^((95-88+12.04)/10) = 80.2 W. Tool shows 95.96 dB, 80.2 W.
Reference table
| Change | dB | Example |
|---|---|---|
| Double power | +3.01 | 100 to 200 W |
| 10x power | +10.00 | 10 to 100 W |
| Double distance | -6.02 | 4 m to 8 m |
| 10x distance | -20.00 | 1 m to 10 m |
Limits
- Free-field only. Room gain excluded.
- One speaker assumed; arrays differ.
- Sensitivity ratings vary by maker method.
- Hearing safety needs exposure math too.
Common mistakes
- Ignoring distance loss entirely.
- Expecting double watts to double loudness.
- Trusting sensitivity without method notes.
- Running amps into clipping for targets.
- Measuring SPL with phone mics as truth.
Try it yourself
Quick checks. Answers sit tucked under each question.
90 dB sens, 50 W, 3 m, target 90?
10 log 50 = 16.99. 20 log 3 = 9.54. SPL 90 + 16.99 - 9.54 = 97.45 dB. Target 90 needs 9 W.
85 dB sens, 200 W, 6 m, target 92?
10 log 200 = 23.01. 20 log 6 = 15.56. SPL 85 + 23.01 - 15.56 = 92.45 dB. Target 92 needs 180.4 W.
Questions
How is seat loudness figured?
Sensitivity + 10 log watts - 20 log meters. Here 88 + 20 - 12.04 = 95.96 dB.
How many watts for my target?
Invert the form: 10^((target - sens + 20 log d)/10). Here 80.2 W for 95 dB.
What happens twice as far?
Minus 6.02 dB per doubling: 95.96 at 4 m falls to 89.94 at 8 m.
How does more power help?
Plus 10 dB per tenfold watts, plus 3.01 per doubling. Diminishing returns rule audio power.
What is sensitivity rated at?
1 W at 1 m on axis, the datasheet reference behind sensitivity figures.
Do rooms change this?
Yes. Rooms add reflections over free-field math, so real seats read a few dB hotter.
Sources
- HyperPhysics: Inverse Square Law for Sound (6 dB rule)
- HyperPhysics: Sound Intensity Problems (worked 6 dB)