RF unit converter

dBm expresses an absolute power level relative to 1 mW. For an average power $P$, divide by that reference before taking the logarithm:

The ratio inside the logarithm has no units. A level of 0 dBm therefore means 1 mW; 10 dBm means ten times that power. dBW uses the same calculation with a 1 W reference.

To convert between power and voltage, the tool needs the load resistance $R$ in ohms. The average power dissipated in a positive real resistance is:

Here $V_{\mathrm{rms}}$ is RMS voltage in volts and $P$ is in watts. This relationship applies to any waveform across that resistance. Converting RMS to peak or peak-to-peak voltage assumes a sine wave. The voltage levels dBV, dBmV and dBµV reference RMS voltage to 1 V, 1 mV and 1 µV respectively.

Gain and loss compare two levels. For input power $P_{\mathrm{in}}$ and output power $P_{\mathrm{out}}$ in the same units, the power ratio in dB is:

An output larger than the input gives positive dB; a smaller output gives negative dB. Equal powers give 0 dB.

For voltage, power depends on voltage squared, so the voltage ratio uses a factor of 20:

Use the same voltage convention and units for input and output. The absolute-value bars compare magnitudes without phase. This voltage ratio equals the power ratio in dB only when the input and output resistances are equal.