# Decibel (voltage) (dBV)

A voltage decibel (dBV) is a unit of measurement of the ratio of an amount of voltage V to V0 = 1 volt given by the formula 20 log10(V/ V0) = 20 log10(V).

For example, the consumer audio level of -10 dBV means

-10 = 20 log10(V)

and so V = (10^(-10/20)) = 0.31623 volts approximately. Thus, the voltage levels used in consumer audio are 0.31623 V. Similarly, if some voltage is equal to 1 volt then its dBV measure is 20 log10(1) = 0 dBV.

The formula for this voltage decibel measure is exactly the same as the regular measure of decibels (dB), except that dBV is specific to measuring electrical potential difference (voltage) and is fixed to the reference 1 V. Thus, this is simply a measure of voltage.

Since the unloaded decibel (dBu) is also a measurement of voltage, there is a direct relationship between dBV and dBu. The dBV measure of a voltage V is 20 log10(V) and the dBu measure of voltage is 20 log10(V / 0.7746). Thus, the amount of voltage is equal to (10^(dBV measure / 20)) and the dBu measure of that voltage would be 20 log10 ((10^(dBV measure / 20)) / 0.7746) = dBV measure + 20 log10(1 / 0.7746) = dBV measure + 2.21845. In short

dBu measure = dBV measure + 2.21845

For example, -10 dBV = -10 + 2.21845 = -7.78155 dBu.

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