The decibel is not a unit of sound. It is a ratio between two intensities, expressed logarithmically, with a reference point at the quietest sound a healthy ear can detect.
dB = 10 × log₁₀(I ÷ I₀), where I₀ = 1 × 10⁻¹² W/m²
An intensity of one microwatt per square metre is 60 decibels, which is ordinary conversation. The decibel calculator also reports that this is a million times the reference intensity, which is the number the scale exists to compress.
Three and ten
Double the intensity and the level goes from 60 to 63 decibels. Not 120, and not 66: three. That is because log₁₀(2) is about 0.3, and ten times that is 3.
Multiply the intensity by ten instead and the level goes from 60 to 70 decibels. Those two numbers, three for a doubling and ten for a tenfold increase, are the whole scale, and everything else follows from them. Four times the power is 6 decibels, a hundred times is 20, a thousand is 30.
The practical consequence is that adding a second identical speaker to a first does almost nothing audible. It doubles the acoustic power and adds 3 decibels, which is around the smallest change most listeners notice. Getting something that sounds meaningfully louder takes roughly ten times the power, and that is where the rule of thumb comes from that a 10 decibel increase is perceived as about twice as loud.
Distance does the same work for free
Sound spreads over the surface of an expanding sphere, so intensity falls with the square of distance. The inverse square law calculator puts an intensity of 100 at 2 metres down to 25 at 4 metres: double the distance, quarter the intensity, which is a drop of 6 decibels.
Ten times the distance is a hundredth of the intensity, or 20 decibels. Moving from 1 metre to 10 metres away takes an intensity of 100 down to 1, and it costs nothing. For noise control that is usually the cheapest intervention available, and it is why distance is the first thing considered on a worksite and amplification the last.
Why it matters beyond audio
Hearing damage is cumulative in energy rather than in level, so a 3 decibel increase halves the safe exposure time. That is the reason occupational limits are written as a level paired with a duration rather than as a level alone, and the reason an apparently small increase in a workplace reading is taken seriously.
The same logarithmic handling turns up wherever a quantity spans many orders of magnitude, which is also why pH is a logarithm and why microbial kill is quoted in logs rather than percentages. For sound that is moving rather than merely loud, the Doppler effect calculator handles the frequency side.