dB Calculator (Decibels, dBm and dBV)
Choose a conversion, enter a number and read the answer. Power ratios use 10 log10, voltage and amplitude ratios use 20 log10, dBm is relative to 1 mW and dBV is relative to 1 V.
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Formula
- Power ratio:
dB = 10 × log10(P2 / P1), back:ratio = 10^(dB / 10) - Voltage or amplitude ratio:
dB = 20 × log10(V2 / V1), back:ratio = 10^(dB / 20) - dBm:
dBm = 10 × log10(P / 1 mW), soP = 10^(dBm / 10) mW - dBV:
dBV = 20 × log10(V / 1 V), soV = 10^(dBV / 20) V
Worked example
- A power ratio of 2:
10 × log10(2) = 3.0103 dB. - A voltage ratio of 10:
20 × log10(10) = 20 dB. - 30 dBm:
10^(30 / 10) = 1000 mW, which is 1 W. - 0.1 V:
20 × log10(0.1) = −20 dBV.
Frequently asked questions
How do you convert a power ratio to decibels?
Take 10 times the base-10 logarithm of the ratio. Doubling the power is 10 × log10(2) = 3.01 dB, and a ratio of 100 is 20 dB.
Why do voltage ratios use 20 instead of 10?
Power goes with the square of voltage into the same resistance, and log10(V²) = 2 log10(V). So a tenfold voltage ratio is 20 × log10(10) = 20 dB, the same as a hundredfold power ratio.
How do I convert dBm to milliwatts?
Use P = 10^(dBm / 10) mW. 0 dBm is 1 mW, 20 dBm is 100 mW and 30 dBm is 10^3 = 1000 mW, which is 1 W. Every 3 dBm roughly doubles the power.
What is dBV?
dBV is voltage compared with 1 V: dBV = 20 × log10(V / 1 V). So 1 V is 0 dBV, 0.1 V is -20 dBV and 0.5 V is -6.02 dBV.
Can a decibel value be negative, and what about a ratio of zero?
Yes, a ratio below 1 gives a negative dB value: a ratio of 0.5 in power is -3.01 dB. A ratio of zero or less has no logarithm, so the calculator rejects it. Decibel values are limited to ±300 dB here.