20log10A1A0

20log10(A1/A0) is a formula used to express the ratio between two amplitudes, A1 and A0, in decibels. The formula originates from the logarithmic nature of human perception of sound intensity and electrical signal strength. The expression can be written as 20 multiplied by the common logarithm of the amplitude ratio: 20 × log10(A1 / A0).

In acoustics, the equation is applied to determine sound pressure levels, where A1 might represent a measured sound pressure and A0 the reference pressure of 20 µPa, the standard threshold of human hearing. In electronics, it is used to calculate voltage gain in amplifiers, where A1 denotes the output voltage and A0 the input voltage. The factor 20 derives from the fact that power is proportional to the square of amplitude; thus, a 10‑fold change in amplitude results in a 20‑bel difference.

The decibel scale (dB) is logarithmic, allowing compact representation of very large or very small ratios. Using 20log10(A1/A0), a 10‑fold increase in amplitude corresponds to a 20‑dB increase, while a 100‑fold increase corresponds to a 40‑dB increase. For ratios less than one, the result is negative, indicating attenuation.

This formula is distinct from 10log10(P1/P0), which is used for power ratios. Both formulas stem from the same logarithmic principle but differ by a factor of two because power involves the square of amplitude. The 20log10 amplitude formula is widely employed in audio engineering, telecommunications, and any domain where signal amplitude comparisons are required.