dB to Voltage Ratio Converter

The dB is a dimensionless unit used to express the ratio between two power levels ($P_1$and $P_2$) or voltage levels ($V_1$ and $V_2$). It is used to quantify gain (amplification) or loss (attenuation).

Convenience: Signal chain calculations become additive. If a source has a 10 dB gain and then passes through a 3 dB cable loss, the net change is simply $10 - 3 = 7 dB$.
Power Ratio (Gain/Loss):

$$Gain(dB) = 10 \cdot \log_{10} \left( \frac{P_{out}}{P_{in}} \right)$$

Voltage Ratio (Gain/Loss):

$$Gain(dB) = 20 \cdot \log_{10} \left( \frac{V_{out}}{V_{in}} \right)$$

Note on Voltage ($20 \cdot\log$): The $20 \cdot\log$ formula is only valid if the measurement is taken across points with identical impedance (e.g., $50 \Omega$ or $75 \Omega$). If the impedances differ, the direct power formula ($10 \cdot\log$) must be used.