Decibel Gain Calculator
From an output and an input voltage, get the gain in decibels and the plain voltage ratio — the two numbers that describe how much a circuit boosts or cuts a signal.
This is the 20·log rule
Voltage (and other field quantities) use 20·log10; power ratios use 10·log10. Mixing the two doubles or halves your answer, so keep them apart.
What is a decibel gain calculator?
Voltages in, decibels out
A decibel gain calculator turns two voltages — the signal at the output and the signal at the input — into the gain expressed in decibels (dB), the logarithmic unit engineers use for amplifiers, filters, cables, and audio gear. The decibel scale exists because real signal chains span an enormous range, from microvolts to volts, and because our ears respond logarithmically. Stating a stage as "+26 dB" is far more compact and intuitive than "a voltage ratio of about 20". The calculator also shows the plain ratio so you can see both views of the same number at once.
Enter the output and input voltage to get the decibel gain and the voltage ratio instantly.
One short formula does the work, built from the ratio of the two voltages and a base-10 logarithm.
gain (dB) = 20 × log10(Vout / Vin)First divide the output voltage by the input voltage to get the voltage ratio. Take the base-10 logarithm of that ratio and multiply by 20. The factor is 20 (not 10) because voltage is a field quantity and power goes with voltage squared — the extra factor of two from the square moves into the multiplier.
Suppose an amplifier turns a 1 V input into a 10 V output.
Voltage ratio
Vout / Vin = 10 / 1 = 10 — the output is ten times the input.
Base-10 logarithm
log10(10) = 1 — the exponent that gives ten.
Gain in decibels
20 × 1 = 20 dB — a tenfold voltage gain is exactly +20 dB.
The decibel figure tells you at a glance how a stage behaves. A positive value is gain (the signal grows), a negative value is attenuation (the signal shrinks), and 0 dB means the output equals the input. Two landmarks are worth memorising: +20 dB is a ×10 voltage change and +6 dB is roughly ×2 (precisely 6.0206 dB), so every doubling of voltage adds about 6 dB and every tenfold change adds 20 dB. These add up neatly — a chain of +6 dB and +20 dB stages is +26 dB total, which is why decibels are so convenient for cascaded systems: you sum the dB instead of multiplying ratios. A reading of −6 dB means the output is about half the input, a common figure for a passive divider or a long cable. Because the scale is logarithmic, even a modest dB number can hide a large ratio: +40 dB is ×100 and +60 dB is ×1000. Keep the 20·log convention in mind — it is for voltage; power gains use 10·log and give half the dB for the same underlying change.
The formula is exact, but a couple of practical points are worth keeping in mind.
Voltage gain, matched impedances, and the right reference
This calculator uses the 20·log10 rule for a voltage (amplitude) ratio. For a power ratio use 10·log10, which gives half as many decibels for the same underlying change. The two only agree as a level when the input and output impedances are equal, so a "gain in dB" quoted across mismatched impedances can be ambiguous. Both voltages must be positive amplitudes in the same units; the result is a pure ratio, so a "dBV" or "dBu" reading instead needs a fixed reference voltage rather than your own input.