SizingKitElectronics · levels and ratios
Decibel calculator
Type a ratio and this prints both decibel values it has — the 10 log figure if the quantity was a power and the 20 log figure if it was a voltage, a current or a pressure — rather than picking one and hoping. It also converts a level between dBm, dBW, dBu, dBV and dBµV with the impedance that joins voltage to power stated on the page, and adds a list of independent sources the way they actually add. Free, no account, and the summing box takes as many levels as you can paste into it.
- 100% free
- No signup
- 10 log and 20 log together
- 7 references listed
- Incoherent summing
One ratio, two decibel values
Nothing here is missing information: a ratio genuinely has two decibel values, and which one is right depends on whether the quantity you divided was a power or an amplitude. Both are printed so you can pick knowingly.
The output divided by the input. Below one is a loss.
Signed: a minus is an attenuation.
AS A POWER RATIO — 10 log
3.010 dB
AS AN AMPLITUDE RATIO — 20 log
6.021 dB
| 6 dB as a power ratio | ×3.98107 |
|---|---|
| 6 dB as an amplitude ratio | ×1.99526 |
| Doubling, as power then as amplitude | 3.01 dB then 6.02 dB |
| Halving, as power then as amplitude | −3.01 dB then −6.02 dB |
The factor of two between the two columns is not a convention, it is the square in P = V² ÷ R. Doubling a voltage quadruples the power, so one 6.02 dB voltage step is one 6.02 dB power step describing the same event — the two logarithms exist so that they agree. They disagree only when a voltage ratio is fed through the power formula, which is the single most common decibel error and is silent, because the answer is exactly half.
An absolute level, and every other way of writing it
A suffix turns a ratio into a level by naming what it is a ratio against. Crossing between a voltage suffix and a power suffix needs an impedance, which is the field below and the reason dBu and dBm are not the same unit.
+4 dBu is the studio line level; −10 dBV is the consumer one.
Default 600 Ω — the historic 600 Ω telephone line impedance dBu was derived in.
AS A VOLTAGE
1.2277 V
AS A POWER, IN THAT IMPEDANCE
2.5119 mW
| Against 1 mW | 4.000 dBm |
|---|---|
| Against 1 W | −26.000 dBW |
| Against 0.774597 V | 4.000 dBu |
| Against 1 V | 1.782 dBV |
| Against 1 µV | 121.782 dBµV |
| How much higher any voltage reads in dBu than in dBV | 2.2185 dB |
| Suffix | Reference | Quantity | Logarithm |
|---|---|---|---|
| dBm | 1 mW | power | 10 log |
| dBW | 1 W | power | 10 log |
| dBu | 0.774597 V | voltage | 20 log |
| dBV | 1 V | voltage | 20 log |
| dBµV | 1 µV | voltage | 20 log |
| dB SPL | 20 µPa | sound pressure | 20 log |
| dBFS | digital full scale | sample amplitude | 20 log |
the reference level each suffix names — dB with no suffix is a ratio and has no reference at all. dB SPL takes 20 µPa as the reference sound pressure, per IEC 61672 and ISO 1683. dBFS has no physical reference: full scale is the largest number the word length can hold, so every real signal is negative on that scale. Modern audio is voltage-driven: outputs are a few hundred ohms or less and inputs are 10 kΩ or more, so no milliwatt is being transferred at all. RF work is 50 Ω, video and some broadcast paths 75 Ω, loudspeakers 4 to 8 Ω nominal. The power column above is only real if that impedance is: at a modern line output driving a 10 kΩ input, the milliwatt dBm counts has nowhere to go, and the dBu figure is the meaningful one.
Adding sources that are not related to each other
Decibels do not add. Convert each one back to a power, add the powers, and take the logarithm of the total — which is what happens below.
Four fans, four amplifier channels, four noise measurements — anything whose sources are independent of one another.
SUM, INCOHERENT
75.67 dB
IF THEY WERE IN PHASE INSTEAD
80.89 dB
| Sources read | 4 |
|---|---|
| Loudest one on its own | 72.00 dB |
| What everything else added to it | 3.67 dB |
| Two equal sources, incoherent then in phase | 3.01 dB then 6.02 dB |
Two equal independent sources add 3.01 dB, not 6 dB and certainly not double the number. That is why silencing the second-loudest of four fans usually changes almost nothing, and why the loudest one is nearly always the whole job. The in-phase column is the other extreme and applies only when the sources are the same signal arriving twice — two amplifier channels fed identically, or a reflection off a hard wall.
How to get a decibel figure right the first time
Three questions decide every decibel answer: a ratio of what, against what, and added how.
Decide whether you divided powers or amplitudes
Watts, milliwatts and acoustic intensity are powers and take 10 log. Volts, currents, sound pressures and sample values are amplitudes and take 20 log. The page shows both columns because the same input number legitimately produces two answers, and the wrong one is exactly half the right one — a mistake nothing in the arithmetic will flag.
If there is a letter after the dB, find its reference
dBm is against 1 mW, dBV against 1 V, dBu against 0.774597 V and dB SPL against 20 µPa. A plain dB has no reference and is a ratio only. Getting from a voltage suffix to a power suffix requires an impedance, so put yours in the impedance field rather than accepting the 600 Ω that dBu was historically derived in.
Add sources through the powers, never through the decibels
Paste the levels into the summing box and it converts each back to a power, adds those, and takes the logarithm of the total. Two equal independent sources give 3.01 dB more than one, not 6 dB and not double the number — which is why quieting anything but the loudest source in a group is usually wasted effort.
Technical specifications
| Two conventions, always both | 10 log for power quantities and 20 log for amplitude quantities, printed side by side — the second is exactly twice the first because P = V² ÷ R |
|---|---|
| References carried | dBm (1 mW), dBW (1 W), dBu (0.774597 V), dBV (1 V), dBµV (1 µV), dB SPL (20 µPa per IEC 61672 and ISO 1683) and dBFS (digital full scale) |
| dBu reference derivation | √(1 mW × 600 Ω) computed in the page rather than transcribed as 0.7746, so the digits cannot drift from the definition |
| Fixed offset between dBu and dBV | 20 log 0.774597 = −2.2185 dB, in every circuit, at every impedance — the two references differ by a constant because both are voltages |
| Studio and consumer line level | +4 dBu is 1.228 V and −10 dBV is 0.316 V, so the gap between them is 11.79 dB rather than the 14 the labels imply |
| Impedance default | 600 Ω, editable and marked as historical — modern audio outputs drive high-impedance inputs and transfer no defined milliwatt at all |
| Summing | Incoherent: 10 log Σ 10^(L/10). Coherent: 20 log Σ 10^(L/20). Two equal sources give +3.01 dB and +6.02 dB respectively |
| Privacy | Measurement levels you paste in are summed in the tab and never transmitted |
Frequently asked questions
Why do some decibel formulas use 10 and others 20?
Because power is proportional to the square of an amplitude, and the logarithm of a square is twice the logarithm. The decibel was always defined on power ratios; the 20 log form is the same definition applied after substituting V² ÷ R for P, with the resistance canceling out. So the two are not alternative conventions to choose between — they are one convention applied to two kinds of quantity, and they agree about what a doubling means.
What is the difference between dBu and dBV?
Only the reference voltage: dBV is against 1 V and dBu is against 0.774597 V, so any level is 2.2185 dB higher when expressed in dBu than in dBV, always. That odd reference is √(1 mW × 600 Ω) — the voltage that would put a milliwatt into a 600 Ω telephone line — and it survived the impedance it came from. dBu is a voltage reference today and carries no impedance at all.
Is +4 dBu really 14 dB hotter than −10 dBV?
No, it is 11.79 dB hotter, and the difference matters when you are matching gear. +4 dBu is 1.228 V and −10 dBV is 0.316 V, a voltage ratio of 3.883. The 14 comes from subtracting the two numbers as if they shared a reference, which they do not — the 2.2185 dB offset between dBu and dBV accounts for the whole discrepancy.
Can I convert dBm to volts?
Only if you state an impedance, because dBm is a power and a power becomes a voltage only across a known resistance. In 600 Ω, 0 dBm is 0.7746 V; in 50 Ω the same 0 dBm is 0.2236 V. That is why lab and RF instruments state 50 Ω on the front panel, and why treating dBm and dBu as interchangeable is only safe in a 600 Ω circuit — which almost nothing built in the last forty years is.
How do I add two noise measurements together?
Convert each back to a power, add the powers, and take the logarithm of the sum — never add the decibel figures. Two independent 70 dB sources make 73.01 dB, three make 74.77 dB, and ten make 80 dB. The corollary is the useful part: a 70 dB source next to a 60 dB one gives 70.41 dB, so the quiet one is effectively invisible and there is no point spending money on it.
When do sources add 6 dB instead of 3 dB?
When they are correlated — the same signal arriving by two paths rather than two independent sources. Two amplifier channels fed identical program material, a driver and its reflection off a nearby hard surface, or two antennas carrying the same modulation all add as amplitudes and give 6.02 dB. Anything genuinely independent, which includes two motors, two fans and two rooms of conversation, adds as powers and gives 3.01 dB.
Why is dBFS always negative?
Because full scale is the largest number the word length can hold, so it is a ceiling rather than a physical reference and every real signal sits below it. Zero dBFS is the maximum, not a nominal level, and it has no fixed relationship to any voltage until a converter's own specification supplies one — which is why an interface's datasheet states something like +18 dBu at 0 dBFS, and why that figure differs between manufacturers.
About the two logarithms, the suffix that names a reference, and why levels do not add
The decibel was invented to make cable losses add up. A telephone circuit is a chain of sections, each multiplying the signal by some fraction, and multiplying a long chain of fractions is tedious where adding a chain of logarithms is not — so the loss of a mile of cable became a number you could total on paper. Everything about the unit follows from that origin. It is a ratio, so it means nothing on its own; it is logarithmic, so it adds where the underlying quantities multiply; and it is a tenth of a bel because a whole bel, a factor of ten, was too coarse a step for the job.
The 10-versus-20 split is not a second convention. The definition is always on power, and the 20 log form is the same expression after substituting V² ÷ R — the square comes out of the logarithm as a factor of two and the resistance cancels, which is precisely why a voltage ratio and the power ratio it causes give the same decibel figure. The error people actually make is running an amplitude ratio through the power formula, and what makes it dangerous is that the result is exactly half rather than obviously wrong: a genuine 12 dB of gain reported as 6 dB looks entirely plausible on a spec sheet. That is the reason this page prints both columns rather than asking you to choose, and it is the same reason the impedance calculator prints polar and rectangular together — the ambiguity is in the quantity, not in the reader.
Suffixes are where the real trouble lives, because a suffix quietly converts a ratio into an absolute level by naming a reference. dBm names one milliwatt and is a power; dBu names 0.774597 V and is a voltage; the two coincide only in 600 Ω, which is the impedance the second reference was derived in and essentially nothing modern uses. In a contemporary audio path the output impedance is low and the input impedance is high, so no defined power is being transferred at all and the voltage reference is the only one with meaning — but instruments and manuals still print both. Finally, levels never add as levels: independent sources add as powers, for 3.01 dB from a pair, and correlated ones add as amplitudes, for 6.02 dB. It is the first of those that governs a room full of fans, which is why the bathroom fan CFM calculator is a sone-and-airflow decision rather than an arithmetic one, and why the air changes per hour calculator sizes the airflow before anybody argues about the noise. On the electrical side, the voltage divider calculator turns a wanted attenuation in decibels into the two resistors that produce it, and the Ohm’s law calculator supplies the power a voltage and a resistance imply before any of this is expressed as a ratio.
Where these levels are summed
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Noise readings and equipment levels pasted into the summing box are parsed and totalled in the page. Nothing identifies a site or a piece of equipment, and nothing is retained once the tab closes.