This tool converts from dBu to Vrms (root-mean-square voltage). Units are Volt/millivolt/microvolt/nanovolt RMS.
Formula
VRMS = 10(dBu / 20) x 0.7746
Background
What is dBu?
dBu is the RMS voltage relative to 0.7746.
1 VRMS is therefore equivalent to 20*Log10(1/0.7746) = 2.218 dBu.
The inverse relationship or conversion from dBu to VRMS is defined by the formula VRMS = 10(dBu / 20) x 0.7746.
Note: dBu is different from dBV which is the RMS voltage relative to 1 Volt.
Where does 0.7746 come from?
It is the value of voltage that dissipates 1 milliwatt (mW) into a 600 ohm load. Reference: Wikipedia article on dB Voltage
V = √(600Ω * 0.001W) Volt
Why 600 ohm?
600 ohm is used in the world of audio systems. Here is a bit of history by Frank McClatchie from his post.
“Early on, engineers discovered that that in order to deliver the maximum amount of audio power to the receiving terminal at all frequencies, it was necessary to match the end of line “load” to the characteristic impedance of a twisted pair wires and also match that impedance to the audio source driving impedance.
Long twisted pair 16 gauge audio transmission wires were found to exhibit impedances in the vicinity of 600 Ohms at voice and musical frequencies up to 15 kHz, so of course the source of the audio and the load at the receiving site must also be 600 Ohms in order to achieve maximum power transfer to the receiving equipment. Since at that time there was power loss on the twisted wire cable it was necessary to apply a vacuum tube amplifier at each end of the transmission wires. Yes, that’s right the 600 Ohm standard originated in the days of vacuum tubes.”
600 ohms are seldom used today with the exception of in high performance headphones.
Practical Applications
Some headphones like the one from Beyerdynamic offer multiple impedance options of 18 Ω, 32 Ω, 80 Ω, 250 Ω and 600 Ω.
The lower impedance devices are better suited for use with smartphones, tablets, MP3 players and laptops while the higher impedance headphones are better suited for high performance professional studio mixing applications and stereo systems. The latter type of systems can provide a higher level of output voltage.
To understand this better, let’s consider a 1 VRMS output signal into two different headphones. One with the impedance of 18 Ω and the other with 600 Ω.
The power delivered to the headphone in each case is calculated as:
P = VRMS2/R
P18 = (1)2/18 = 55 mW
P600 = (1)2/600 = 1.6 mW
The power delivered to the headphone with 18 Ω impedance is more than 30 times that delivered to the headphone with 600 Ω impedance.
To deliver the same level of power (55 mW) into 600 Ω, VRMS should be 5.77 Volt.
Reference: What impedance should I choose for my headphones?
Example Calculation
The Scarlett Solo amplifier has a headphone output level of 7 dBu. This translates to VRMS = 1.73 Volt.