Decibel Gain Calculator
V
V
Gain20.0000 dB
Ratio10.0000×
The Decibel Gain Calculator expresses how much an amplifier or stage boosts a signal, in decibels. Gain in dB is a logarithmic ratio of output to input, which is why cascaded stages add up so neatly. Pick voltage gain or power gain, enter the input and output levels, and the tool returns the gain in dB along with the plain linear ratio. A negative result means the stage attenuates rather than amplifies.
Formula
Voltage: dB = 20 × log10(Vout / Vin); Power: dB = 10 × log10(Pout / Pin)
- Vout / Vin
- Output-to-input voltage ratio
- Pout / Pin
- Output-to-input power ratio
- dB
- Gain in decibels (negative when attenuating)
How it works
- Choose voltage gain or power gain with the mode switch, depending on whether you are measuring volts or watts.
- Enter the output level and the input level in the same units; their ratio drives the calculation.
- For voltage the calculator takes 20 times the base-ten logarithm of the ratio, and for power it takes 10 times the logarithm, then also reports the linear ratio.
Worked example
An amplifier raises a signal from 0.5 V to 5 V (voltage gain mode).
- Ratio = 5 ÷ 0.5 = 10.
- Gain = 20 × log10(10) = 20 × 1 = 20 dB.
A tenfold voltage increase is a gain of 20 dB.
Frequently asked questions
- Why is voltage gain 20·log and power gain 10·log?
- Power is proportional to voltage squared, and the logarithm of a square brings the factor of two out front. So 20 times the log of the voltage ratio gives the same decibel figure as 10 times the log of the matching power ratio.
- What does a negative dB gain mean?
- A negative value means the output is smaller than the input, so the stage attenuates the signal. For example a voltage ratio of 0.1 gives -20 dB.
- How many dB is doubling a signal?
- Doubling voltage is about 6 dB (20·log10 2), while doubling power is about 3 dB (10·log10 2). These round figures are handy rules of thumb for quick estimates.
- Why must the levels be positive?
- The decibel formula relies on the logarithm of the output-to-input ratio, which is only defined for positive numbers, so both input and output must be greater than zero.