A point source in the open radiates onto an expanding sphere. Double the radius and the same power is spread over four times the area, so the intensity falls to a quarter — and a quarter of the energy is −6 dB. That is the whole law, and it is worth being able to say in one breath: every doubling of distance costs 6 decibels.

Written out: $L_2 = L_1 - 20\log_{10}\!\left(\dfrac{r_2}{r_1}\right)$ — L-two equals L-one minus twenty log of r-two over r-one. $L_1$ is the level measured at the near distance $r_1$, $L_2$ the level at the further distance $r_2$; both distances in the same unit, because only their ratio matters. The coefficient is 20, not 10, because distance acts on pressure and the level is defined on pressure squared. Use 10 by habit and you halve every drop.

Two numbers are worth memorising outright. A factor of two in distance is 6 dB. A factor of ten is 20 dB. Between them they cover almost every boundary question a site meets, and they run backwards just as well: to lose 20 dB, get ten times as far away.

When there is no measurement to start from, the machine's own rating will do. $L_p = L_W + 10\log_{10}\!\left(\dfrac{Q}{4\pi r^{2}}\right)$, where $L_W$ is the sound power level in dB re 1 pW, $L_p$ the sound pressure level at distance $r$ in metres, and $Q$ the directivity factor: 1 in free space, 2 standing on hard ground, 4 in the corner of two walls, 8 in a three-way corner. The $4\pi r^{2}$ is the surface of the sphere the power is spread across, and $Q$ says what fraction of that sphere the sound is actually confined to — put a machine in a corner and the same power has a quarter of the space to fill.

A handy special case, and the boss will hand it to you: on hard ground at 1 m, $10\log_{10}\!\left(\dfrac{2}{4\pi}\right) = -7.98$, so $L_p \approx L_W - 8$. In free space at 1 m it is $L_W - 11$.

What this law is not: it is a free-field law. Indoors, once you are past the critical distance, the reverberant field takes over and the level stops falling no matter how far you walk. Outdoors it also ignores ground effect, air absorption over long ranges, wind and temperature gradients, and every barrier. Use it on open site, where it is honest, and be suspicious of it in a plant room.