Decibel Calculator: dB, dBm, Power Ratio and Voltage Ratio

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How to use this tool

Choose the mode that matches what you actually have in front of you. If your figure carries a letter after the dB, such as dBm or dBW, it is an absolute level and there is a fixed reference behind it. If it is a bare dB, it is a ratio between two things and it means nothing until you say what those two things are.

The input people get wrong is picking ten log when they should have picked twenty. If the two quantities you are comparing are powers, use the power ratio mode. If they are voltages, currents, sound pressures or any other amplitude, use the voltage ratio mode. Choose wrong and your answer is out by exactly a factor of two in dB, which is the single most common decibel error there is.

What the calculation is doing

A decibel is a logarithm of a ratio, scaled by ten. For power, dB equals ten times the base ten log of the ratio. That is the definition, and everything else follows from it.

The twenty log form is not a second definition. Power in a resistor goes as voltage squared over resistance, so if you double the voltage you quadruple the power. Put a squared term inside a logarithm and it comes out as a factor of two in front, so ten log of the power ratio becomes twenty log of the voltage ratio. Same rule, rearranged. The factor of twenty is doing the squaring for you.

This is why doubling power is 3 dB and doubling voltage is 6 dB. Both are correct and they describe different physical changes. Ten log of 2 is 3.0103, twenty log of 2 is 6.0206. The round numbers everyone quotes are those two values with the decimals dropped, which is fine for a rule of thumb and worth knowing about when a calculation does not quite close.

Adding the letter turns the ratio into a level. The m in dBm means the reference is one milliwatt, so 0 dBm is exactly 1 mW, no ratio required. Because the reference is fixed, dBm figures describe real powers and you can add and subtract them freely along a signal chain. That is the practical reason the unit exists: gains and losses that would need multiplying and dividing become additions and subtractions.

Why a level in dBm needs an impedance before it becomes a voltage

A power figure on its own does not fix a voltage. Power is voltage times current, and the split between them depends on the resistance the signal is working into. Say a level is 0 dBm and you still cannot put a voltmeter reading to it until you say across what.

At 50 ohms, the standard for RF and test equipment, 0 dBm is 0.2236 volts rms. At 75 ohms, used for video and aerial feeds, the same 0 dBm is 0.2739 volts. At 600 ohms, the old telephone and audio line standard, it is 0.7746 volts. Identical power, three different voltages, because the impedance changed.

That 0.7746 figure is worth recognising, because it became the reference for dBu in audio. Zero dBu is the voltage that one milliwatt produces in 600 ohms, and once the industry moved to voltage bridging the impedance stopped mattering but the odd looking reference stuck. That is why professional audio gear runs at plus 4 dBu, which is 1.228 volts rms, and why dBu and dBV differ by a constant 2.2185 dB.

A worked check you can repeat on paper

Start with the default, 30 dBm. Subtract the 30 that converts dBm to dBW and you have 0 dBW, and 0 dBW is one watt by definition. So 30 dBm is exactly 1 W. Take another 10 off and you get 20 dBm, which is one tenth of a watt, 100 mW. Every ten dB is a factor of ten in power, so you can walk the scale in your head without a calculator.

Now a ratio. An amplifier turns 5 mW into 500 mW. The power ratio is 100, and ten log of 100 is 20, so the gain is 20 dB. Check it in levels instead: 5 mW is 6.9897 dBm and 500 mW is 26.9897 dBm, and the difference is 20 dB. Two routes, same answer, which is the point of working in levels.

Then the voltage trap. That same amplifier raises voltage by a factor of ten, not a hundred, because power goes as voltage squared and the square root of 100 is 10. Twenty log of 10 is also 20 dB. The dB figure is the same either way, which is exactly the design intent, but the underlying ratios are 100 and 10. Anyone who reports a voltage ratio of 100 for a 20 dB amplifier has used the wrong formula.

One more, into a load. Take 0 dBm at 50 ohms. Power is 1 mW, which is 0.001 W. Voltage is the square root of power times resistance, so the square root of 0.001 times 50, which is the square root of 0.05, which is 0.2236 volts. Read it back the other way with V squared over R and you get 0.05 squared over 50, back to 0.001 W. The tool runs both directions and they agree to twelve figures.

Mistakes that catch people out

Using ten log on a voltage. The classic. If your two numbers are voltages and you use the power formula, every answer is exactly half what it should be. The tell is a gain figure that looks suspiciously modest for the numbers involved.

Adding dBm figures together. You can add a gain in dB to a level in dBm, and you can subtract two dBm levels to get a gain in dB. You cannot add two dBm levels. Two 30 dBm sources do not make 60 dBm, they make 33 dBm, because two watts is 3 dB above one watt.

Quoting a bare dB as though it means something absolute. A specification that says the noise floor is minus 90 dB is incomplete. Minus 90 dB relative to what? Without a reference it could be dBm, dBFS, dBc or something else entirely, and the difference between them is the difference between a usable spec and a meaningless one.

Mixing dBu and dBV. They are both voltage references and they sit 2.2185 dB apart. Consumer gear runs at minus 10 dBV, professional gear at plus 4 dBu, and the gap between those two is not 14 dB as the arithmetic suggests but 11.79 dB once the references are lined up. That mismatch is behind a great many hum and level problems.

Assuming 3 dB is exactly double. It is 1.995 times, not 2. Ten log of 2 is 3.0103 dB. The approximation is harmless once, but chain twenty stages together and the drift is real, which is why the tool carries the exact value rather than the rounded one.

How this was checked

The engine was written twice and compared. Anchor points first: 0 dBm returns 0.001 W exactly, 30 dBm returns 1 W, and 1 W returns 30 dBm. A power ratio of 2 gives 3.0103 dB and a voltage ratio of 2 gives 6.0206 dB, which are the standard values. Zero dBm converts to 0.223607 V at 50 ohms, 0.273861 V at 75 ohms and 0.774597 V at 600 ohms.

The dBu reference was derived from one milliwatt into 600 ohms rather than typed in as 0.7746, and it comes out at 0.774597. Reading it back as dBV gives minus 2.2185 dB, matching the published offset. Round trips were run at minus 100, minus 30, 0, 13, 30 and 60 dB through every mode and every impedance, and all returned to the starting value within one part in a billion.

Popular conversions

Each link opens the tool with that figure already loaded, in the right mode.

dBm to watts. -120 dBm to watts · -110 dBm to watts · -100 dBm to watts · -90 dBm to watts · -80 dBm to watts · -70 dBm to watts · -60 dBm to watts · -50 dBm to watts · -40 dBm to watts · -30 dBm to watts · -25 dBm to watts · -20 dBm to watts · -15 dBm to watts · -10 dBm to watts · -7 dBm to watts · -5 dBm to watts · -3 dBm to watts · 0 dBm to watts · 3 dBm to watts · 5 dBm to watts · 7 dBm to watts · 10 dBm to watts · 13 dBm to watts · 15 dBm to watts · 17 dBm to watts · 20 dBm to watts · 23 dBm to watts · 25 dBm to watts · 27 dBm to watts · 30 dBm to watts · 33 dBm to watts · 36 dBm to watts · 40 dBm to watts · 43 dBm to watts · 46 dBm to watts · 50 dBm to watts · 53 dBm to watts · 56 dBm to watts · 60 dBm to watts

Watts to dBm. 0.000001 W to dBm · 0.00001 W to dBm · 0.0001 W to dBm · 0.001 W to dBm · 0.005 W to dBm · 0.01 W to dBm · 0.05 W to dBm · 0.1 W to dBm · 0.25 W to dBm · 0.5 W to dBm · 1 W to dBm · 2 W to dBm · 3 W to dBm · 5 W to dBm · 10 W to dBm · 15 W to dBm · 20 W to dBm · 25 W to dBm · 50 W to dBm · 100 W to dBm · 200 W to dBm · 500 W to dBm · 1000 W to dBm

dB to a power and voltage ratio. -40 dB to ratio · -30 dB to ratio · -20 dB to ratio · -15 dB to ratio · -12 dB to ratio · -10 dB to ratio · -9 dB to ratio · -6 dB to ratio · -5 dB to ratio · -4 dB to ratio · -3 dB to ratio · -2 dB to ratio · -1 dB to ratio · 0 dB to ratio · 1 dB to ratio · 2 dB to ratio · 3 dB to ratio · 4 dB to ratio · 5 dB to ratio · 6 dB to ratio · 9 dB to ratio · 10 dB to ratio · 12 dB to ratio · 15 dB to ratio · 20 dB to ratio · 25 dB to ratio · 30 dB to ratio · 40 dB to ratio · 50 dB to ratio · 60 dB to ratio

A ratio expressed in dB. 0.1 x to dB · 0.25 x to dB · 0.5 x to dB · 0.75 x to dB · 1 x to dB · 1.5 x to dB · 2 x to dB · 2.5 x to dB · 3 x to dB · 4 x to dB · 5 x to dB · 10 x to dB · 20 x to dB · 50 x to dB · 100 x to dB · 1000 x to dB

dBm to volts rms. -60 dBm to volts · -40 dBm to volts · -30 dBm to volts · -20 dBm to volts · -10 dBm to volts · 0 dBm to volts · 10 dBm to volts · 13 dBm to volts · 20 dBm to volts · 30 dBm to volts · 40 dBm to volts · 50 dBm to volts

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