Electrical · Free Calculator
Decibel (dB) Calculator
Convert between decibels and power or voltage ratios, and between dBm and milliwatts.
Power ratioVoltage ratiodBmGain and loss
dB
Ratio in dB20 dB
20 dB as ratio100 ×
How this result was calculated
- dB = 10 × log₁₀(ratio) = 20 dB
- Ratio = 10dB ÷ 10 = 100
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Decibel Formulas
Power: dB = 10 × log₁₀(P2 ÷ P1)
Voltage: dB = 20 × log₁₀(V2 ÷ V1)
dBm = 10 × log₁₀(P ÷ 1 mW)
Voltage: dB = 20 × log₁₀(V2 ÷ V1)
dBm = 10 × log₁₀(P ÷ 1 mW)
Worked example
A power gain of 100 is 20 dB, while a voltage gain of 100 is 40 dB. 1 W is 30 dBm.
Key insight: 3 dB is a doubling of power, 6 dB a doubling of voltage. A filter’s cutoff frequency is where the output is 3 dB down.
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Frequently Asked Questions
Why is voltage dB 20 log and power 10 log?
Power is proportional to voltage squared, and the square becomes a factor of two in the logarithm.
What is dBm?
Power relative to 1 milliwatt. 0 dBm = 1 mW, 30 dBm = 1 W.
What does −3 dB mean?
Half the power, or 70.7 % of the voltage.
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