dB / dBm Converter

Why two different formulas

Decibels always compare powers:

When you compare voltages on the same impedance, power goes with $V^2$, so the same definition becomes $20{\log }_{10}(V_2/V_1)$ — that's the whole mystery of 10 vs 20. A handy anchor set: 3 dB ≈ ×2 power, 6 dB ≈ ×2 voltage, 20 dB = ×10 voltage = ×100 power. dBm is an absolute level referenced to 1 mW, so converting it to volts requires the impedance: $V_{\text{rms}}=\sqrt{P\cdot Z}$ — 0 dBm is 224 mV RMS in a 50 Ω system but 775 mV in 600 Ω audio land.