dB, dBm, dBW and Watt Converter

What is a decibel?

The decibel (dB) expresses the ratio of two quantities on a logarithmic scale. It turns very large and very small ratios into handy numbers and lets you add successive gains instead of multiplying them.

• Power ratio: dB = 10 × log10(P2 / P1)
• Voltage or current ratio: dB = 20 × log10(V2 / V1)

Figures worth remembering: twice the power is 3 dB, ten times is 10 dB and a hundred times is 20 dB. Twice the voltage is 6 dB and ten times is 20 dB.

dBm and dBW

Because a decibel is a ratio, it does not give an actual power. It does once the reference is fixed:

• dBm: referred to 1 milliwatt. 0 dBm = 1 mW, 20 dBm = 100 mW, 30 dBm = 1 W.
• dBW: referred to 1 watt. dBW = dBm − 30.

Conversion: dBm = 10 × log10(P / 1 mW) and back again P = 1 mW × 10^(dBm / 10).

dBµV and impedance

Voltage levels are often given in dBµV: dBµV = 20 × log10(V / 1 µV). 1 mV is 60 dBµV. Converting that to dBm needs the system impedance, because power is V² / Z. In a 50 Ω system dBm = dBµV − 107, and in a 75 Ω system dBm = dBµV − 108.75.

Gain chains

The effects of amplifiers, cables and attenuators along a signal path add up in decibels. With an input of −10 dBm followed by a 20 dB amplifier, 3 dB of cable loss and a 15 dB second amplifier, the output is −10 + 20 − 3 + 15 = 22 dBm, which is 158 mW.

Limits

The 20 × log relation for voltage ratios matches the power gain only when the impedance is the same at both points. The chain calculation assumes matched stages. Sound pressure level (dB SPL) uses a different reference. See the sound level calculator for that.