Amplifier Gain Calculator
Calculate amplifier gain in decibels (dB) from voltage, current, or power ratios.
Convert between dB and linear gain values.
Amplifier gain is a measure of how much a circuit amplifies an input signal. It is expressed either as a dimensionless ratio (output divided by input) or in decibels (dB), which is a logarithmic scale that makes it easier to work with the very large and very small numbers that appear in electronics.
Gain formulas:
Voltage gain (Av):
- Linear: Av = Vout / Vin
- In dB: Av(dB) = 20 × log₁₀(Vout / Vin)
Current gain (Ai):
- Linear: Ai = Iout / Iin
- In dB: Ai(dB) = 20 × log₁₀(Iout / Iin)
Power gain (Ap):
- Linear: Ap = Pout / Pin
- In dB: Ap(dB) = 10 × log₁₀(Pout / Pin)
Why decibels? The dB scale makes multiplication into addition, which is extremely useful for cascaded systems (amplifiers in series). Instead of multiplying gains together, you simply add their dB values.
Common dB reference values:
| dB | Voltage / Current Ratio | Power Ratio |
|---|---|---|
| 0 dB | 1× | 1× |
| 3 dB | 1.41× | 2× |
| 6 dB | 2× | 4× |
| 10 dB | 3.16× | 10× |
| 20 dB | 10× | 100× |
| 40 dB | 100× | 10,000× |
| 60 dB | 1,000× | 1,000,000× |
| -3 dB | 0.707× | 0.5× (half power — the “half-power point”) |
| -6 dB | 0.5× | 0.25× |
| -20 dB | 0.1× | 0.01× |
The -3dB point: In amplifier and filter design, the -3dB point marks where gain has fallen to 70.7% of its maximum voltage value (or 50% of power). This is the standard definition of an amplifier’s bandwidth. A filter or amplifier “cuts off” at its -3dB frequency.
Cascaded stages: If Amplifier A has a gain of 20dB and Amplifier B has a gain of 15dB, the combined gain is simply 35dB — much easier than multiplying linear ratios (10× and 5.62× = 56.2×).