Speaker SPL and amp watts calculator.

How loud will a speaker be at a given wattage and distance?

Sensitivity is the SPL (dB, relative to 20 µPa) produced at 1 W of electrical input, measured at 1 metre. From there, level = sensitivity + 10 × log₁₀(watts) − 20 × log₁₀(distance in metres). The 10 log term is the standard decibel power ratio: doubling the power adds about 3 dB. The distance term is the inverse-square law for a point source: each doubling of distance loses 6.02 dB.

Worked example. A 90 dB speaker driven with 100 W: 90 + 20 = 110 dB SPL at 1 m, and at 4 m 98.0 dB (a drop of 12.0 dB). To reach 100 dB at 1 m the same speaker needs 10 W; at 2 m it needs 40 W, four times as much.

A 3 dB more sensitive speaker needs half the power. A speaker 3 dB more sensitive produces very nearly double the sound power for the same electrical input, so it reaches the same level on half the amplifier wattage.

Limits and hearing. This is a free-field estimate for one speaker. Rooms add reflected sound, several speakers add, and music has peaks well above its average level, so leave generous amplifier headroom. Noise exposure can cause a permanent hearing loss, and noise-induced hearing loss is cumulative, so treat high estimated levels with care.