dB and dBm calculator: watts, volts and ratios

Watts to dBm and back, the voltage that power puts across a load, the same level in dBW, dBV and dBµV, and any gain or loss as a power ratio, a voltage ratio and in decibels, with the reference each figure is measured against stated rather than assumed.

Fig 1 — 8.00 W is +39.03 dBm. Each 10 dB step on the top row is ten times the power, but only √10 = 3.16 times the voltage across 50.0 Ω.

Convert

Value

Unit

Load resistance R (Ω)

dBm · dBW: +39.03 dBm · +9.03 dBW
Power: 8.00 W
Voltage across 50.0 Ω: RMS · peak · peak-to-peak: 20.0 V · 28.3 V · 56.6 V
dBV · dBµV of that RMS voltage: +26.02 dBV · +146.02 dBµV

How this is calculated

Standard: BIPM SI Brochure, 9th edition, Table 8 note (m); Infineon AP24026 formula appendix

$L_P = 10 \lg\frac{P_1}{P_0}\ \text{dB}, \qquad L_V = 20 \lg\frac{V_1}{V_0}\ \text{dB}$: SI Brochure: m = 10 lg(X/X₀) for a power-like quantity; Infineon: "Power [dB] = 10 log(P1/P0)" and "Voltage [dB] = 20 log (V1/V0)". The factor of two comes from power going as voltage squared across the same resistance.
$P_{\text{dBm}} = 10 \lg\frac{P}{1\ \text{mW}}, \qquad V_{\text{dB}\mu\text{V}} = 20 \lg\frac{V}{1\ \mu\text{V}}$: Infineon AP24026: "P[dBmW or dBm] = 10 log(P1/1mW); dBm is defined for a 50Ohm system", and "V[dBµV] = 20 log(V1/1µV)". dBW (against 1 W) is dBm − 30; dBV (against 1 V) is dBµV − 120.
$V_{\text{RMS}} = \sqrt{P\,R}, \qquad V_{pp} = 2\sqrt{2}\,V_{\text{RMS}}$: The voltage a power puts across the load R, and its peak-to-peak value for a sine. The dBm of a power does not depend on R; the voltage does.
$L_A = \ln\frac{A_2}{A_1}\ \text{Np}, \qquad 1\ \text{Np} = 20 \lg e\ \text{dB} \approx 8.686\ \text{dB}$: SI Brochure: the neper for amplitude ratios, n = ln(A2/A1). Its equivalent in decibels follows from the two definitions.

Assumptions

Voltages are RMS; peak and peak-to-peak values assume a sine.
Converting between power and voltage uses the load resistance entered, 50 Ω by default, the system Infineon defines dBm for.
A voltage ratio in dB assumes both voltages are across the same impedance, so the power ratio is its square.
Levels are stated against their reference, as the SI Brochure requires: 1 mW for dBm, 1 W for dBW, 1 V for dBV, 1 µV for dBµV.

What a decibel figure actually says

A decibel is a ratio written as a logarithm. The SI Brochure lists the bel and the decibel among the units "used to express the values of logarithmic ratio quantities whose numerical values are based on the decadic logarithm … usually applied to logarithmic power ratios", and defines the statement L = m dB to mean m = 10 lg(X/X₀). Ten decibels is therefore a factor of ten in power, twenty is a factor of a hundred, and every multiplication in a signal chain becomes an addition, which is the whole reason engineers put up with logarithms.

Voltage is different, and the difference is the most common mistake in the subject. Power across a fixed resistance goes as the square of the voltage, so the same change in dB is a smaller factor in volts. Infineon's EMC design guide writes both forms side by side: "Power [dB] = 10 log(P1/P0)" and "Voltage [dB] = 20 log (V1/V0)". A factor of two in voltage is 6.02 dB, the same 6.02 dB as a factor of four in power; ten decibels is ten times the power but only √10, 3.16 times, the voltage. Both rows of the figure above sit on the same axis to show exactly that.

A ratio needs no reference; a level does. The SI Brochure is blunt that "it is important that the quantity be specified, and that any reference value used be specified", and the letters after "dB" are how the reference is stated. Infineon defines the two that matter most on a bench: "P[dBmW or dBm] = 10 log(P1/1mW)", power against one milliwatt, and "V[dBµV] = 20 log(V1/1µV)", voltage against one microvolt, the unit EMC emission limits are drawn in. The same arithmetic gives dBW against one watt, which is just dBm minus 30, and dBV against one volt, which is dBµV minus 120.

Converting between a power level and a voltage level needs one more thing: the resistance the power is delivered into. Infineon notes that "dBm is defined for a 50Ohm system", the impedance of RF and test equipment, and the calculator defaults to 50 Ω. The dBm figure of a power does not depend on it; the volts that power produces do. One milliwatt, 0 dBm, is 224 mV RMS across 50 Ω and 775 mV across the 600 Ω that older audio work assumes.

dBm to watts chart

Common dBm levels as power and as the RMS and peak-to-peak voltage of a sine across 50 Ω, computed by the calculator above. Every 10 dB is a decade of power and every 3 dB very nearly doubles it; 20 dB is ten times the voltage.

Level	Power	V RMS, 50 Ω	V peak-to-peak, 50 Ω
−30 dBm	1.00 µW	7.07 mV	20.0 mV
−20 dBm	10.0 µW	22.4 mV	63.2 mV
−10 dBm	100 µW	70.7 mV	200 mV
0 dBm	1.00 mW	224 mV	632 mV
+3 dBm	2.00 mW	316 mV	893 mV
+6 dBm	3.98 mW	446 mV	1.26 V
+10 dBm	10.0 mW	707 mV	2.00 V
+13 dBm	20.0 mW	999 mV	2.83 V
+17 dBm	50.1 mW	1.58 V	4.48 V
+20 dBm	100 mW	2.24 V	6.32 V
+23 dBm	200 mW	3.16 V	8.93 V
+27 dBm	501 mW	5.01 V	14.2 V
+30 dBm	1.00 W	7.07 V	20.0 V
+33 dBm	2.00 W	9.99 V	28.3 V
+37 dBm	5.01 W	15.8 V	44.8 V
+40 dBm	10.0 W	22.4 V	63.2 V
+43 dBm	20.0 W	31.6 V	89.3 V
+47 dBm	50.1 W	50.1 V	142 V
+50 dBm	100 W	70.7 V	200 V

Watts to dBm chart

The other direction, for the powers people actually convert: a radio module's output, an amplifier's rating, a transmitter's limit.

Power	dBm	dBW
1.00 mW	+0.00 dBm	−30.00 dBW
10.0 mW	+10.00 dBm	−20.00 dBW
100 mW	+20.00 dBm	−10.00 dBW
250 mW	+23.98 dBm	−6.02 dBW
500 mW	+26.99 dBm	−3.01 dBW
1.00 W	+30.00 dBm	+0.00 dBW
2.00 W	+33.01 dBm	+3.01 dBW
5.00 W	+36.99 dBm	+6.99 dBW
8.00 W	+39.03 dBm	+9.03 dBW
10.0 W	+40.00 dBm	+10.00 dBW
20.0 W	+43.01 dBm	+13.01 dBW
50.0 W	+46.99 dBm	+16.99 dBW
100 W	+50.00 dBm	+20.00 dBW

dB to power and voltage ratio chart

The decibel values that come up in gain, loss and filter figures, as the power ratio and the voltage ratio each stands for. Negative decibels are the reciprocals: −3 dB is half the power and 0.707 of the voltage, the corner of every first-order filter on this site.

dB	Power ratio	Voltage ratio
+1 dB	× 1.259	× 1.122
+2 dB	× 1.585	× 1.259
+3 dB	× 1.995	× 1.413
+6 dB	× 3.981	× 1.995
+10 dB	× 10	× 3.162
+20 dB	× 100	× 10
+30 dB	× 1000	× 31.62
+40 dB	× 1.00 × 10^+4	× 100
+60 dB	× 1.00 × 10^+6	× 1000
−3 dB	× 0.5012	× 0.7079
−6 dB	× 0.2512	× 0.5012
−10 dB	× 0.1	× 0.3162
−20 dB	× 0.01	× 0.1
−40 dB	× 1.00 × 10^-4	× 0.01

Adding up a signal chain in dB

The reason decibels exist is that gains and losses multiply, and a logarithm turns multiplication into addition. A level in dBm plus a gain in dB is a new level in dBm; a gain in dB plus a loss in dB is the net gain in dB. The chain below is summed that way, one row per stage, and the page's own arithmetic multiplies the same stages as linear power ratios to check it.

Stage	Adds	Level after it	Power
Source, 0 dBm	+0 dBm	+0 dBm	1.00 mW
Cable and connectors	−3 dB	−3 dBm	501 µW
Amplifier	+20 dB	+17 dBm	50.1 mW
Attenuator pad	−10 dB	+7 dBm	5.01 mW

Multiplied out, 1 mW × 0.501 × 100 × 0.1 is 5.01 mW, the same answer as the last row, reached without a single multiplication by the dB column. That is also where the rule about what may be added comes from: a gain adds to a level, a gain adds to a gain, but two levels never add in dB. Two 0 dBm signals combined give 2 mW, which is +3 dBm, not 0 dBm and not +0 dBm + 0 dBm.

Worked example: 8 W to dBm, and Infineon's 100 µV

The default is 8 W, one of the values most often typed into a search box, into 50 Ω; and Infineon's own example of a voltage level.

8 W       10 × lg(8 W / 1 mW)    = 10 × lg(8000)  = +39.03 dBm      = +9.03 dBW
          V RMS across 50 Ω      = √(8 × 50)      = 20.0 V         (56.6 V peak-to-peak)
5 dBm     1 mW × 10^(5/10)                         = 3.16 mW
100 µV    20 × lg(100 µV / 1 µV) = 20 × lg(100)    = 40 dBµV        (Infineon's example)
× 2 V     20 × lg(2)                               = +6.02 dB = × 4 in power

The first line shows why dBm is convenient: a power that spans eight orders of magnitude on a bench, from a microwatt of leakage to a hundred watts of amplifier, fits in −30 to +50. The last line is the relation to keep in mind: whenever a figure is quoted in dB, the question is whether it describes power or amplitude, because the factor behind it differs by a square.

Where the decibel figure stops meaning what it seems

A level without its reference is not a number. "40 dB" of noise, of attenuation or of signal says nothing until the reference is named, which is the SI Brochure's point. dBm, dBW, dBV and dBµV are four different scales; a figure moved from one to another without the offset between them is wrong by 30, 60 or 120 dB.

Voltage dB assumes the same resistance at both ends.The 20 lg rule holds for a voltage ratio only when both voltages are across the same impedance, so that the power ratio is the square of the voltage ratio. An amplifier with a 10 kΩ input and a 50 Ω output has a voltage gain in dB that is not its power gain in dB.

RMS, and a sine. The calculator converts power to voltage as an RMS value and gives peak and peak-to-peak for a sine. A square wave, a pulse or noise has a different peak for the same RMS, and the peak-to-peak row does not apply to it.

Nepers. The SI Brochure pairs the decibel with the neper, a natural-logarithm unit for amplitude ratios, n = ln(A₂/A₁). The calculator gives it for completeness; one neper of amplitude ratio is 20·lg e, 8.686 dB. It appears in transmission-line attenuation, and rarely elsewhere.

Common decibel mistakes

Using 10 lg on a voltage ratio. A factor of two in voltage is 6 dB, not 3; 3 dB is a factor of two in power, a factor of 1.41 in voltage.
Dropping the reference. dBm and dBW are 30 dB apart; dBV and dBµV are 120 dB apart. A spectrum in dBµV compared with a limit in dBm without the 50 Ω conversion between them is compared with the wrong line.
Adding dBm values. Two 0 dBm signals combine to +3 dBm of power, not 0 dBm + 0 dBm; levels add as powers, ratios add as dB. A gain in dB is added to a level in dBm; two levels are not added to each other.
Forgetting the load. dBm to volts is only defined once the resistance is known; the same 0 dBm is 224 mV in 50 Ω and 775 mV in 600 Ω.
Reading −3 dB as "the signal is gone". It is half the power and 71 % of the voltage, which is why a filter's corner frequency is where the signal is still easily visible.