dB (Voltage)

dB = 20 × log₁₀(V2/V1)

Quick answer

This calculator solves dB = 20 × log₁₀(V2 / V1) for Gain. With Reference Voltage 12 V, Measured Voltage 26.4 V, the result is 6.848 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Gain (dB)
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
dB Gain dB dB
V1 Reference Voltage V pV, nV, µV, mV, V, kV
V2 Measured Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Reference Voltage 12 V, Measured Voltage 26.4 V
  2. 2. The relation: dB = 20 × log₁₀(V2 / V1)
  3. 3. Substitute: V1 = 12 V, V2 = 26.4 V
  4. 4. Result: Gain = 6.848 dB

Worked examples

Minimum range

Given: Reference Voltage 0.33 V, Measured Voltage 0.726 V

Result: Gain = 6.848 dB

Low range

Given: Reference Voltage 3.3 V, Measured Voltage 7.26 V

Result: Gain = 6.848 dB

Typical

Given: Reference Voltage 12 V, Measured Voltage 26.4 V

Result: Gain = 6.848 dB

High range

Given: Reference Voltage 0.23 kV, Measured Voltage 0.506 kV

Result: Gain = 6.848 dB

Maximum range

Given: Reference Voltage 2.3 kV, Measured Voltage 5.06 kV

Result: Gain = 6.848 dB

Solving for each variable

Solve for Gain

Reference Voltage 0.33 V, Measured Voltage 0.726 V → 6.848 dB

Solve for Reference Voltage

Gain 0.3 dB, Measured Voltage 0.726 V → 0.7014 V

Solve for Measured Voltage

Gain 0.3 dB, Reference Voltage 0.33 V → 0.3416 V

How Gain changes with Reference Voltage

Reference Voltage (input) Gain (result)
1.2 V 26.85 dB
3 V 18.89 dB
6 V 12.87 dB
9 V 9.347 dB
12 V 6.848 dB
18 V 3.327 dB
24 V 0.8279 dB
48 V -5.193 dB
84 V -10.05 dB
120 V -13.15 dB

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Frequently asked questions

How do you calculate dB (Voltage)?

Use dB = 20 × log₁₀(V2 / V1). With Reference Voltage 12 V, Measured Voltage 26.4 V, Gain works out to 6.848 dB.

What is the formula for dB (Voltage)?

The formula is dB = 20 × log₁₀(V2 / V1). When expressing voltage ratios in decibels, the multiplier is 20 instead of 10.

How do you find Reference Voltage when you know the other values?

Rearrange for Reference Voltage: with Gain 0.3 dB, Measured Voltage 0.726 V, Reference Voltage is 0.7014 V.

How do you find Measured Voltage when you know the other values?

Rearrange for Measured Voltage: with Gain 0.3 dB, Reference Voltage 0.33 V, Measured Voltage is 0.3416 V.

Related Concepts

All Signal & dB formulas →
dB (Power) dB (Voltage) dBm to Watts dBV (Voltage Level) dBu (Voltage Level) dBm to dBW Conversion Receiver Noise Floor Effective Number of Bits

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