Enter two positive voltage magnitudes to calculate voltage gain in dB, or enter a dB gain to find the missing input or output voltage.
Table of contents
How to use our Decibel Voltage Gain Calculator
- Choose "Calculate dB gain", "Solve output voltage", or "Solve input voltage" based on the value you need.
- Select the shared "Voltage unit" used by your meter, oscilloscope, simulation, or datasheet.
- Enter the two visible values. Use positive voltage magnitudes, and enter a signed value in "Voltage gain (dB)" when that field is shown.
- Click "Calculate". Check the ratio: above 1 means gain, below 1 means attenuation, and 1 means unity gain.
Definitions
Decibel (dB): A logarithmic way to express a ratio. For voltage gain, this calculator uses 20 times the base-10 logarithm of the output-to-input voltage ratio. [1]
Voltage ratio (V/V): Output voltage divided by input voltage. It has no physical unit because both voltages use the same unit.
Gain: Output voltage magnitude is greater than input voltage magnitude. The ratio is above 1 and the dB value is positive.
Attenuation: Output voltage magnitude is lower than input voltage magnitude. The ratio is below 1 and the dB value is negative.
Unity gain: Input and output voltage magnitudes are equal. The ratio is 1 and the gain is 0 dB.
Voltage magnitude: A positive measurement, such as RMS, peak, or peak-to-peak voltage. Both values must use the same measurement convention.
Common mistakes and quick fixes
Mistake: Using 10 times the base-10 log of a voltage ratio.
Fix: Use 20 times the base-10 log for voltage or amplitude ratios. The factor of 10 is used for power ratios.
Mistake: Entering the input in V and the output in mV.
Fix: Select one "Voltage unit" and enter both values in that unit. Changing the unit selector converts existing voltage entries.
Mistake: Entering a negative waveform sample.
Fix: Enter a positive RMS, peak, peak-to-peak, or other voltage magnitude. A negative sample can show phase or polarity, not a negative magnitude.
Mistake: Comparing RMS voltage at one point with peak voltage at another.
Fix: Use the same measurement convention for both values before finding the ratio.
Mistake: Treating voltage dB as power gain when impedances differ.
Fix: Read this as a voltage or amplitude result. Calculate power gain separately when input and output impedances are different.
Limitations & Key Assumptions / Boundary Conditions
- Use positive voltage magnitudes only. Zero and negative magnitudes are outside the logarithmic equation's domain.
- Measure both voltages using the same convention, such as both RMS or both peak-to-peak. Mixing conventions changes the ratio.
- The result describes voltage magnitude only. It does not show phase, polarity, or signal inversion.
- Voltage gain is not automatically the same as power gain. A power comparison needs the relevant input and output impedance information.
- Supported entered gain is from -600 dB through 600 dB. Values outside that range can create unusably extreme numerical results.
- Load conditions, frequency response, meter accuracy, noise, and measurement bandwidth can make measured gain differ from a nominal specification.
Methodology
Calculation
The calculator first finds the output-to-input voltage ratio from two positive voltage magnitudes expressed in the same selected unit.
Voltage ratio = output voltage / input voltage
It converts that ratio to decibels with the standard voltage-ratio relationship. [1]
Voltage gain (dB) = 20 x log10(output voltage / input voltage)
For a known dB gain, it first converts dB back to a linear voltage ratio, then uses that ratio to solve the missing voltage.
Voltage ratio = 10^(voltage gain in dB / 20)
Output voltage = input voltage x voltage ratio
Input voltage = output voltage / voltage ratio
Worked example
With an input of 1 V and an output of 2 V, the voltage ratio is 2. The gain is 20 x log10(2), or 6.021 dB after rounding to three decimal places. With an input of 0.5 mV and a gain of 20 dB, the ratio is 10, so the required output is 5 mV.
Reading the result
A positive dB value means the output magnitude is larger, a negative value means it is smaller, and 0 dB means equal magnitudes. This is a voltage or amplitude calculation; comparing power requires impedance information when the input and output impedances differ.