dB conversion: dBFS, dBu, dBV, dBm and dB SPL

A decibel is always a ratio to something. That is the whole of it, and it is also why dB conversions go wrong so often: the unit name tells you which reference was used, and if you ignore that suffix you are quietly comparing a voltage against a sound pressure or against digital full scale. The arithmetic is then correct and the answer is meaningless.

This article covers the five references you meet in audio work, where the odd 0.775 V figure comes from, and the two conversions that genuinely cannot be done without extra information. The converter below does all of them at once so you can see how the numbers move together.

The five references at a glance

Every row below answers a different question. Only two of them describe a voltage in absolute terms.

Unit	Reference	Measures	Needs an extra assumption
dBFS	Digital full scale	Amplitude relative to the largest code	Yes — the voltage that equals 0 dBFS
dBV	1 V rms	Voltage	No
dBu	0.775 V rms	Voltage	No
dBm	1 mW	Power	Yes — the impedance
dB SPL	20 µPa	Sound pressure	Yes — microphone sensitivity

Where 0.775 V comes from

dBm was defined first, as power relative to 1 mW. When telephone engineering settled on 600 Ω as a standard line impedance, 1 mW into 600 Ω became the reference voltage:

That is the origin of the 0.775 V figure rounded onto every datasheet since. dBu ("u" for unloaded) keeps the same reference voltage but drops the impedance requirement, which is why modern equipment can quote levels in dBu without anyone caring what it is connected to. At exactly 600 Ω the two units are numerically identical — the converter shows both rows agreeing when the impedance field is left at 600.

dBFS is not a voltage

dBFS is the one unit that lives entirely inside the digital domain: 0 dBFS is the largest code the converter can represent, and everything else is negative. Nothing in that definition tells you how many volts leave the box, because that depends on the analogue stage behind the converter. This is why the converter above asks for a full-scale output: with the default 1.228 V rms (+4 dBu), a signal at 0 dBFS also reads +4 dBu, and −20 dBFS reads −16 dBu. Change the full-scale field to 2 V rms and both of those voltage figures shift, while the dBFS reading stays where it is.

One rounding note, because it looks like a bug the first time you see it. +4 dBu is exactly 1.2277 V rms, while the field ships with the widely quoted 1.228 V. That 0.0003 V difference moves the answer by 0.002 dB, which is orders of magnitude below any real measurement uncertainty — but it is why, with the default left in place, the converter prints 4.0025 dBu on the row where the text says +4 dBu.

A related trap: values above 0 dBFS do exist in floating-point DSP and in inter-sample peaks after resampling. They are not errors in the maths, but they will be clipped the moment they reach a fixed-point output stage.

Three worked examples

1. A console meter reads +4 dBu. What is that in volts and in dBV? Ten to the power of 4/20 is 1.585, times 0.775 V gives 1.228 V rms. Against the 1 V reference that is 20·log10(1.228) = +1.78 dBV. So +4 dBu = 1.228 V rms = +1.78 dBV — the 2.22 dB offset between the two units, always in the same direction, because 0.775 V is below 1 V.

2. A 24-bit recording peaks at −6 dBFS on a converter whose full-scale output is +4 dBu. What voltage is that? First the amplitude ratio: 10^(−6/20) = 0.501. Times 1.228 V rms gives 0.615 V rms. In dBu that is 20·log10(0.615/0.775) = −2.0 dBu. The short form is simpler: −6 dBFS relative to a +4 dBu reference is 4 − 6 = −2 dBu, because both scales are amplitude ratios against the same denominator.

3. A measurement microphone with 50 mV/Pa sensitivity outputs 0.775 V rms. What sound pressure level is that? Divide the voltage by the sensitivity: 0.775 / 0.05 = 15.5 Pa rms. Against 20 µPa that is 20·log10(15.5 / 2×10⁻⁵) = 117.8 dB SPL. The shortcut version, worth memorising for acoustic work, is SPL = measured dBV − microphone sensitivity in dBV/Pa + 94 dB. Here that is −2.2 − (−26.0) + 94 = 117.8 dB SPL.

Five mistakes that survive a decade of experience

1. Adding levels that have different references. Adding two dB values is only valid when both use the same reference. Summing two uncorrelated signals of equal level gives +3 dB; the same signals summed coherently give +6 dB. Neither result comes from adding dBFS to dBu.
2. Treating peak and RMS as interchangeable. For a sine wave the peak is 3.01 dB above the RMS value, so mixing the two across a calculation introduces a silent 3 dB error. Decide which one your meter reports before you start.
3. Assuming dBm means dBu. They coincide only into 600 Ω. Into 50 Ω the reference voltage is √(0.001 × 50) = 0.224 V, and the same power reads about 10.8 dB higher in dBm terms than its voltage suggests.
4. Using 1 V or 0.775 V as a digital full-scale reference by default. Full-scale output is a property of the specific device. If it is not documented, measure it, or state the assumption explicitly in the report.
5. Forgetting that dB SPL needs a sensitivity. A voltage at a microphone output is not a sound level until you divide by the microphone's sensitivity. Two microphones on the same preamp, one at 12.6 mV/Pa and one at 50 mV/Pa, will differ by 12 dB for the same acoustic input.

Formulas worth keeping

Quantity	Conversion
Amplitude ratio → dB	20 · log10(A / Aref)
Power ratio → dB	10 · log10(P / Pref)
dB → amplitude ratio	10 ^ (dB / 20)
dB → power ratio	10 ^ (dB / 10)
dBm reference voltage	√(0.001 · R)
dB SPL from voltage	20 · log10(V / (sens × 20 µPa))
RMS from peak (sine)	Vpk / √2

Summary

Use dBV and dBu when you mean a voltage, dBm when you mean a power into a stated impedance, dB SPL when you mean sound pressure, and dBFS when you mean distance from digital clipping. Convert through one intermediate quantity — volts RMS is the convenient choice — and name your assumptions for the two conversions that need them. The converter above is deliberately built the same way.

Values produced here are engineering aids rather than measurements; the conditions under which they are valid are described in the disclaimer. Related tools are listed in the tool index.