Speaker power and SPL calculator
Doubling amplifier power buys 3 dB. Getting a speaker 3 dB more sensitive buys the same, for nothing.
dB at 1 W, 1 m
W
dB
dB
Sound pressure level at the listener
101.47dB
- Power for the target plus headroom
- 225.5 W
- SPL if you double the power
- 104.48 dB
- SPL at half the distance
- 107.49 dB
- Loss from distance
- 9.54 dB
- Gain from amplifier power
- 20.00 dB
- Gain from multiple speakers
- 3.01 dB
Show the working
- Speaker sensitivity = 88
- Amplifier power = 100
- Listening distance = 3
- Number of speakers = 2
- Target SPL = 95
- Headroom for peaks = 10
- Gain from amplifier power = 10 * log10(100) = 20
- Loss from distance = 20 * log10(3) = 9.542 43
- Gain from multiple speakers = 10 * log10(2) = 3.0103
- Sound pressure level at the listener = 88 + 20 - 9.542 43 + 3.0103 = 101.468
- needed_gain = 95 + 10 - 88 + 9.542 43 - 3.0103 = 23.5321
- Power for the target plus headroom = 10^(23.5321/10) = 225.534
- spl_at_peak = 101.468 = 101.468
- SPL if you double the power = 101.468 + 3.0102999566398 = 104.478
- SPL at half the distance = 101.468 + 6.020599913279624 = 107.488
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- SPL = sensitivity + 10 log10(power) - 20 log10(distance) + 10 log10(speakers)
- the inverse square law costs 6 dB per doubling of distance
Ten times the power is only 10 dB, which sounds roughly twice as loud. Amplifier power is an expensive way to buy volume.
Sensitivity ratings are measured anechoically. A real room adds several dB back from reflections.