How loud will it be?
A speaker’s loudness at your listening position depends on four things: its sensitivity, the amplifier power, the distance and the number of speakers.
The formula
SPL = sensitivity + 10 × log10(P) − 20 × log10(d) + 10 × log10(n)
- sensitivity: the level in dB measured at 1 m with 1 W (often written 1 W/1 m, or 2.83 V/1 m for 8 Ω speakers);
- P: amplifier power per speaker in watts;
- d: distance in meters;
- n: number of speakers playing the same signal.
The key rules
- Doubling the power adds only 3 dB. Going from 50 to 100 W gives 3 dB more, a modest increase.
- 10 times the power adds 10 dB, which sounds about twice as loud.
- Doubling the distance loses 6 dB in free field (inverse square law). Indoors, room reflections reduce this loss, often to 3 or 4 dB.
- A second speaker adds 3 dB.
- Sensitivity matters a lot: a 92 dB speaker needs less than half the power of an 88 dB speaker for the same level.
Example
Two speakers with 88 dB sensitivity, 50 W each, heard from 10 ft (3.05 m):
- one speaker: 88 + 17.0 − 9.7 ≈ 95.3 dB;
- two speakers: about 98.3 dB.
To reach 100 dB at that distance, each speaker needs about 74 W, or about 150 W with 3 dB of headroom for peaks.
Headroom
Music has short peaks 10 to 20 dB above its average level. Amplifiers that clip on peaks sound harsh and can damage tweeters. Allow at least 3 dB, ideally 10 dB, of headroom over the average level you want.
Real-world limits
- The formula gives the maximum level if the speaker can take that power. Check the speaker’s power handling and maximum SPL.
- Speakers compress at high power: the real gain falls a few dB short.
- Placing a speaker against a wall or in a corner can add 3 to 6 dB of bass.
Protect your hearing
Long exposure above 85 dB can damage hearing. At 100 dB, the safe exposure time is about 15 minutes a day. Keep levels reasonable for long listening sessions.