Why Decibels Use Different Formulas for Power vs. Amplitude
Decibels express a ratio on a logarithmic scale, but the exact formula depends on whether you're comparing power or amplitude (voltage/current) quantities — a detail that trips up a lot of people converting by hand. Power ratios use dB = 10log10(P1/P2); voltage or current ratios use dB = 20log10(V1/V2) — the factor-of-two difference exists because power is proportional to the square of voltage or current, and that squaring becomes a factor of 2 once pulled out of the logarithm.
This is exactly why "+3dB" means "double the power" but "+6dB" means "double the voltage" — both describe a doubling, just of different underlying quantities, and mixing them up produces a real, meaningful error, not just a rounding difference. Decibels exist in the first place because they compress an enormous dynamic range (audio power can span factors of a trillion or more between the quietest and loudest sounds) into a much more manageable additive scale, and because gains/losses through a chain of components can simply be added in dB rather than multiplied as raw ratios.
Getting power vs. voltage dB conversions right matters directly for audio engineering, RF link budgets, and any signal chain where components' specifications are given in dB and need to combine correctly.