Speaker SPL Calculator (Loudness from Sensitivity, Power and Distance)
Sound level in dB at the listening position from the speaker's sensitivity, the power, the distance and the number of speakers — or the power needed for a level you want.
Results
The dashed line marks the value you entered.
What this tool does
Sensitivity is the level a speaker makes at 1 m for 1 W (some makers quote 2.83 V, which equals 1 W only into 8 Ω). Add 3 dB for each doubling of power, take off 6 dB for each doubling of distance in the open air, and add 3 dB for each doubling of identical speakers playing uncorrelated sound. Two speakers fed the same signal can add up to 6 dB close to the centre line, so this is the cautious figure. Indoors the level stops falling at 6 dB per doubling once reverberation takes over, so this is a free-field estimate. Music peaks sit well above its average level, so leave generous headroom in the amplifier.
Formula
SPL = sensitivity + 10 log₁₀(P) − 20 log₁₀(d) + 10 log₁₀(n) (free field, 1 W / 1 m sensitivity)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sn | Speaker sensitivity (dB at 1 W, 1 m) | dB |
pw | Power into each speaker | W |
d | Distance from the speakers to the listener | m |
n | Number of identical speakers | — |
tg | Level you want (to find the power needed) | dB |
SP | Sound level at the listener | dB |
S1 | Sound level at 1 m | dB |
DL | Level lost to distance | dB |
PN | Power needed per speaker for the wanted level | W |
Worked example
- Speaker sensitivity (dB at 1 W, 1 m)90 dB
- Power into each speaker50 W
- Distance from the speakers to the listener3 m
- Number of identical speakers2
- Sound level at the listener100.5 dB
- Sound level at 1 m110.0 dB
- Level lost to distance9.5 dB
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.