Decibel (Voltage Ratio) Calculator
Convert between a voltage ratio and decibels — solve for the gain in dB, or for either voltage — with unit conversion, a live dB-versus-ratio graph, and absolute levels like dBV and dBu.
Every ×10 in voltage adds 20 dB, so the curve is a straight line on a logarithmic ratio axis. The dot marks your V₂/V₁.
How to Use This Calculator
- Choose what to solve for — the gain in dB, the output voltage V₂, or the reference voltage V₁.
- Enter the other two values, picking µV, mV, V or kV for each voltage.
- Check the graph — your operating point is marked on the dB-versus-ratio line.
- Switch to Advanced to see V₁ and V₂ as dBV, dBu, dBmV and dBµV.
- Read the step-by-step solution to check or show your work.
What This Tool Offers
- ✓Solve for dB, V₂ or V₁ from the same voltage-ratio equation.
- ✓Unit conversion between µV, mV, V and kV on every voltage field.
- ✓Live dB-versus-ratio graph with your operating point marked.
- ✓Gain in other forms — nepers, power ratio, and percent change.
- ✓Absolute levels in dBV, dBu, dBmV and dBµV in Advanced mode.
What is a decibel voltage ratio?
The decibel expresses a ratio on a logarithmic scale. For voltages, the gain (or loss) between a reference voltage V₁ and another voltage V₂ is 20 times the base-10 logarithm of their ratio. A ratio of 10 is +20 dB, a ratio of 1 is 0 dB, and a ratio of 0.1 is −20 dB.
Formula
Rearranged: V₂ = V₁ · 10dB/20 and V₁ = V₂ / 10dB/20. The factor is 20 rather than 10 because power is proportional to voltage squared, and log(x²) = 2·log(x).
| Symbol | Meaning |
|---|---|
| dB | Gain (positive) or attenuation (negative), in decibels |
| V₁ | Reference (input) voltage |
| V₂ | Compared (output) voltage |
Reference: common dB values
| dB | Voltage ratio | Power ratio |
|---|---|---|
| −40 | 0.01 | 0.0001 |
| −20 | 0.1 | 0.01 |
| −6 | 0.501 | 0.251 |
| −3 | 0.708 | 0.501 |
| 0 | 1 | 1 |
| +3 | 1.413 | 1.995 |
| +6 | 1.995 | 3.981 |
| +20 | 10 | 100 |
| +40 | 100 | 10,000 |
Reference: absolute voltage levels
| Unit | 0 dB equals |
|---|---|
| dBV | 1 V |
| dBu | 0.7746 V (1 mW into 600 Ω) |
| dBmV | 1 mV |
| dBµV | 1 µV |
Frequently asked questions
10·log₁₀ is for power ratios. Because power scales with the square of voltage (P = V²/R), the same dB value for a voltage ratio needs a factor of 20.
Only when both voltages appear across the same impedance. If the impedances differ, the power ratio also depends on that impedance ratio; the dB value for voltage stays as defined here.
Yes. A negative value means V₂ is smaller than V₁ — an attenuation or loss. Zero dB means the voltages are equal.
Voltage magnitudes are used; signs and phase are ignored in the ratio.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| dB | Decibel (voltage/amplitude ratio level) | dB |
| V₂ | Measured (or output) voltage | V (or same as V₁) |
| V₁ | Reference (or input) voltage | V (or same as V₂) |
| log₁₀ | Common (base‑10) logarithm | — |
What it means
For voltage (or amplitude) ratios, the decibel is defined as 20·log₁₀(V₂/V₁). This arises because power is proportional to voltage squared, so the factor of 2 multiplies the log: 10·log₁₀((V₂/V₁)²) = 20·log₁₀(V₂/V₁). A 20 dB increase means 10 times the voltage, and 6 dB means roughly double. The dB scale for voltage is used in amplifier gains, filter responses, and signal levels. Example: If a signal voltage increases from 1V to 10V, the gain is 20·log₁₀(10/1) = 20 dB. A 6 dB gain corresponds to a voltage ratio of approximately 2 (since 20·log₁₀(2) ≈ 6.02 dB).
Worked example
Decibel Voltage Ratio – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V₂/V₁ | 10 |
| Formula | dB = 20·log₁₀(V₂/V₁) |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
The decibel for voltage or amplitude ratio is 20·log₁₀(V₂/V₁), since power is proportional to voltage squared. This is used to express voltage gains, losses, and levels in circuits. Engineers use it to specify amplifier voltage gain, to measure insertion loss, and to compare signal amplitudes. Like the power dB, it simplifies calculations in RF and audio systems. Understanding the voltage dB is essential for working with filters, amplifiers, and transmission lines.
- Voltage gain and loss calculations in amplifiers and filters
- Insertion loss and return loss measurement
- Audio and RF signal level alignment
- Bode plot frequency response representation
- Educational understanding of voltage decibels
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