Decibel (dB) Gain Calculator
Convert ratio ⇄ dB — 20·log for voltage, 10·log for power.
What it does: Convert between a linear ratio and decibels, distinguishing voltage gain from power gain.
When to use it: When reading amplifier/filter gain, computing cascades, or working with attenuation.
MEANS —
No history yet. Each calculation is automatically saved to this device.
How to use the decibel gain calculator
Choose voltage/power → enter a value and unit → read the conversion.
- 01
Choose voltage or power
Use 20·log for a voltage/amplitude ratio and 10·log for a power ratio — this is the step people most often get wrong.
- 02
Enter a value and pick a unit
Enter a ratio (e.g. 2 = 2× gain) and select "Ratio", or enter a dB figure and select "dB".
- 03
Read the conversion
Both the dB value and the linear ratio are shown; a negative dB means attenuation.
Handy anchors
Remember these few and mental math is enough.
| Voltage (20log) | Power (10log) | |
|---|---|---|
| +3 dB | ×1.41 | ×2 (double) |
| +6 dB | ×2 | ×4 |
| +10 dB | ×3.16 | ×10 |
| +20 dB | ×10 | ×100 |
| −3 dB | ×0.71 | ×0.5 (half-power point) |
dB = 20·log10(amplitude ratio) = 10·log10(power ratio).
Common questions, answered in 3 minutes
Why is voltage 20log and power 10log?
Power is proportional to the square of voltage (P∝V²); taking the log turns the square into a factor of 2, so 10·log(V² ratio)=20·log(V ratio). Thus for the same factor, the voltage dB is twice the power dB.
How is this different from dBm?
dB is gain (a relative, dimensionless ratio); dBm is absolute power (referenced to 1mW). This tool computes "how much gain/attenuation"; to compute an absolute level, use the dBm converter.
How many times is +3dB exactly?
About ×2 in power (this is where the half-power point −3dB=×0.5 comes from); about ×1.41 (√2) in voltage. These are often confused, so be careful whether you mean voltage or power.
What is a negative dB?
Attenuation. For example, −20dB in voltage means the output is 1/10 of the input. This tool accepts negative dB.
How do you compute cascaded gain?
dB values add directly: a +10dB stage cascaded with a +6dB stage = +16dB. This is exactly the convenience of expressing gain in dB.
Standards and sources referenced by this tool
| Item | Value / Formula | Source |
|---|---|---|
| Power gain | dB = 10·log10(P₂/P₁) | Decibel definition |
| Voltage gain | dB = 20·log10(V₂/V₁) | Decibel definition |
Standard decibel definition, no external API. To compute absolute power, use the dBm converter.