20log10I2I1

20log10I2I1 is a notation used to express the ratio of two quantities, I2 and I1, on a logarithmic decibel scale. The expression indicates how much larger or smaller I2 is compared with I1, measured in decibels (dB). The factor 20 appears because the decibel form is most commonly applied to quantities that are proportional to an underlying amplitude (such as voltage, current, pressure, or electric field), rather than to power alone.

In practice, whether this form is used depends on what I represents. If I stands for a quantity proportional to amplitude (for example voltage, sound pressure, or a field strength), then 20 log10(I2/I1) yields a decibel difference appropriate for that amplitude. If I represents power or intensity (energy per unit area), the conventional expression is 10 log10(I2/I1). Since power is proportional to the square of amplitude, 20 log10(I2/I1) can be related to amplitude ratios via the appropriate conversion.

Examples: If I2 is twice I1, then 20 log10(I2/I1) = 20 log10(2) ≈ 6.02 dB. If I2 is half of I1, the value is ≈ -6.02 dB.

Applications include acoustics, electronics, and communications, where relative levels are more meaningful than absolute values. The concept is closely linked to the use of decibels for transfer functions, where the magnitude of a ratio is expressed as 20 log10 of the amplitude ratio or 10 log10 of the power ratio. See also decibel, logarithmic scale, and amplitude versus power measurements.