dB (Voltage)

dB = 20 × log₁₀(V2/V1)

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Result
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Formula

dB = 20 × log₁₀(V2 / V1)

Description

When expressing voltage ratios in decibels, the multiplier is 20 instead of 10. This is because power is proportional to the square of voltage (P = V²/R), and log₁₀(V²) = 2 × log₁₀(V), so the factor of 2 moves from inside the logarithm to outside as a multiplier of 20. This ensures that a given dB value represents the same power ratio regardless of whether it was calculated from power or voltage measurements. A +6dB voltage gain means the voltage has doubled (which corresponds to 4x power, or +6dB in the power formula as well).

Variables

  • dB — Voltage ratio in decibels
  • V1 — Reference voltage in volts (V)
  • V2 — Measured voltage in volts (V)

Practical Notes

The 20× formula assumes equal impedances at the measurement points. If impedances differ (common in RF systems), you must account for the impedance ratio or use power measurements instead. Key landmarks: +6dB = 2x voltage, +20dB = 10x voltage, +40dB = 100x voltage.

Related Formulas

dB (Power) dBm to Watts dBV (Voltage Level) dBu (Voltage Level) dBm to dBW Conversion Receiver Noise Floor

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