Decibel Shield
dB to watts calculator
Decibels measure a power ratio: every 3 dB is about twice the power and every 10 dB is ten times. So a 100 W amplifier needs about 200 W for +3 dB and 1,000 W for +10 dB. Enter a starting power and a change in dB to get the watts, or two powers to get the decibels between them. dBW is power relative to 1 W, so 20 dBW is 100 W.
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Watts after a change in dB
Power after a change of +3 dB
199.5 W
1.995 times the power
dB between two powers
The second is +10.00 dB from the first
dBW and watts
20 dBW = 100 W = 50 dBm
Power decibels: 10 × log10 of the power ratio. +3 dB is about twice the power, +10 dB is ten times.
dB change to power
| Change | Power ratio | From 100 W |
|---|---|---|
| −10 dB | × 0.100 | 10.0 W |
| −6 dB | × 0.251 | 25.1 W |
| −3 dB | × 0.501 | 50.1 W |
| −1 dB | × 0.794 | 79.4 W |
| +1 dB | × 1.26 | 126 W |
| +3 dB | × 2.00 | 200 W |
| +6 dB | × 3.98 | 398 W |
| +10 dB | × 10.0 | 1,000 W |
| +20 dB | × 100 | 10,000 W |
The formula
A change in power in decibels is 10 × log10(P₂ / P₁). Turned around, the new power is P₁ × 10dB/10. Doubling the power is +3.01 dB and ten times the power is +10 dB, whatever the starting power. For absolute power, dBW = 10 × log10(P / 1 W) and dBm = 10 × log10(P / 1 mW), so dBm is always dBW + 30.
Sources: ITU-R Recommendation V.574-5, Use of the decibel and the neper in telecommunications; UNSW Physclips, dB: What is a decibel?; HyperPhysics, Loudness.
Watts, decibels and how loud it sounds
An amplifier's watts and a speaker's loudness are related through decibels, not directly. A 10 dB rise is commonly judged about twice as loud, and that takes ten times the power. That is why going from a 100 W to a 200 W amplifier changes so little: it is a 3 dB step. To see what a level in dB sounds like, use the decibel meter; to turn a speaker's sensitivity and watts into a level at your seat, use the SPL calculator. For powers given in dBm, as radio and Wi-Fi specifications are, the dBm to watts converter has a table from 0 to 60 dBm.
How many watts is 3 dB?
A 3 dB increase is almost exactly twice the power (10^0.3 = 1.995), so 100 W becomes about 200 W and 1 W becomes about 2 W. A 3 dB decrease halves it. Decibels describe a ratio, so "3 dB" has no wattage on its own until you say what it is 3 dB above.
How many watts does it take to sound twice as loud?
About ten times the power. Listeners judge a sound roughly twice as loud when it rises by about 10 dB, and 10 dB is a tenfold power ratio, so a 50 W amplifier needs about 500 W into the same speakers to sound twice as loud. Doubling the power gives only 3 dB, a change most people notice but would not call twice as loud.
What is dBW?
dBW is power in decibels relative to one watt: 0 dBW is 1 W, 10 dBW is 10 W, 20 dBW is 100 W and −30 dBW is 1 mW. It is 30 less than the same power in dBm, which is relative to one milliwatt.
Is the dB to watts conversion the same for voltage?
No. Power uses 10 × log10 of the ratio and voltage, current and sound pressure use 20 × log10, because power goes with the square of the voltage. So doubling the voltage into the same load is +6 dB, which is four times the power.
