dB, Watts & Unit Converter.

Loudness in decibels follows a logarithm of the power ratio, so dB = 10 x log10(B/A). Doubling the power doubles the ratio to 2, and 10 x log10(2) works out to about +3 dB. That is why going from a 500 W amp to a 1000 W amp barely sounds louder; to gain a clearly noticeable 10 dB you need roughly ten times the power.

In a free field (open air, no reflections) sound pressure follows the inverse square law, so every time you double the distance you lose about 6 dB. Halving the distance gains you 6 dB. Indoors, room reflections reduce that loss, so the real-world figure is often gentler than the open-air 6 dB per doubling.

A +3 dB change comes from doubling power, while a +6 dB change comes from doubling voltage or sound pressure (SPL). They are different because power scales with 10 x log10 and voltage or pressure scales with 20 x log10 of the ratio. As a rough rule of thumb, about +10 dB is needed before most listeners perceive a sound as roughly twice as loud.

Multiply metres by 3.28 to get feet, or divide feet by 3.28 to get metres. So a 10 m throw is about 32.8 ft and a 4 m wide stage is about 13.1 ft. This is handy when a rider or fixture spec sheet quotes coverage or rigging heights in imperial units.

Because level rises with 10 x log10 of the power ratio, you need to double the power for every +3 dB. To get a clear +10 dB lift you need roughly ten times the wattage, and +20 dB takes about one hundred times. In practice it is usually cheaper and cleaner to add more or more efficient speakers, or move the audience closer, than to keep chasing loudness with amplifier power alone.