An unloaded decibel (dBu) is a unit of measurement of the ratio of an amount of voltage V to V_{0} = 0.7746 volts given by the formula 20 log_{10}(V/ V_{0}) = 20 log_{10}(V/ 0.7746), where voltage is measured using quadratic mean (also called root mean square, RMS).
For example, the professional audio and studio recording level of +4 dBu means
4 = 20 log_{10}(V/ 0.7746)
and so V = 0.7746 (10^(4/20)) = 1.2283 volts. Thus, the voltage used in professional audio is 1.2238 V. Similarly, if some voltage is equal to 0.7746 then its dBu measure is 20 log_{10}(0.7746 / 0.7746) = 0 dBu.
The formula for this unloaded decibel measure is exactly the same as the regular measure of decibels (dB), except that dBu is specific to measuring electrical potential difference (voltage) and is fixed to the reference 0.7746 VRMS. Thus, this is simply a measure of voltage. The reference point of 0.7746 VRMS was chosen historically as it represented the voltage that produces 1mW of power in a 600W resistor ((0.001 * 600)^(1/2) = 0.7746).
Previously denoted as dBv, this measure is now denoted as dBu to avoid confusion with dBV, which is a similar, but different measure of voltage.
Since the voltage decibel (dBV) is also a measurement of voltage, there is a direct relationship between dBu and dBV. The dBV measure of a voltage V is 20 log_{10}(V) and the dBu measure of voltage is 20 log_{10}(V / 0.7746). We can use these two formulae to express the amount of voltage as 0.7746 (10^(dBu measure / 20)) and the dBV measure as 20 log_{10} (0.7746 (10^(dBu measure / 20))) = dBu measure + 20 log_{10} (0.7746) = dBu measure - 2.21845. In short
dBV measure = dBu measure – 2.22845
For example, +4 dBu = +4 - 2.21845 = 1.78155 dBV.