Decibels to voltage ratio, power ratio, and absolute volts (dBu / dBV) - the conversions behind every gain knob, pad switch, and level spec, with the reference values worth memorizing.
voltage / amplitude
power
RMS · 0 dBu = 0.7746 V
+4 dBu = pro line level
RMS · 0 dBV = 1 V
−10 dBV = consumer line level
Voltage/amplitude: +6 dB = 2×, +20 dB = 10×, −6 dB = ½. Power: +3 dB = 2×, +10 dB = 10×. Loudness: roughly +10 dB = "twice as loud" to human ears. Line levels: pro +4 dBu ≈ 1.23 V, consumer −10 dBV ≈ 0.32 V, difference ≈ 11.8 dB.
Note this page converts electrical and digital levels. dB SPL - sound pressure in the air, what a "70 dB room" means - is the same math referenced to 20 µPa; for measuring that, use the decibel meter.
For amplitude quantities (voltage, sound pressure): ratio = 10^(dB/20), so +6 dB ≈ 2× voltage and +20 dB = 10×. For power quantities: ratio = 10^(dB/10), so +3 dB ≈ 2× power and +10 dB = 10×. The factor-of-two difference exists because power is proportional to voltage squared.
Both express absolute voltage. dBV is referenced to 1 volt; dBu to 0.7746 V (the voltage that dissipates 1 mW in the old 600 Ω telephone standard). Professional line level +4 dBu ≈ 1.23 V; consumer line level −10 dBV ≈ 0.316 V - which is why the pro/consumer difference is about 11.8 dB, not 14.
No - it is twice the voltage (and 4× the power), but perceived loudness roughly doubles per +10 dB. The three scales to keep separate: voltage doubles every 6 dB, power doubles every 3 dB, subjective loudness doubles about every 10 dB.
Decibels relative to digital full scale - the loudest sample a converter can represent is 0 dBFS, and everything below is negative. It measures headroom in a digital system, not voltage: how 0 dBFS maps to volts depends on your interface's calibration (commonly +4 dBu ≈ −18 to −14 dBFS in pro gear).