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Decibel Voltage Ratio Calculator

Turn a voltage ratio into decibels (dB).

How it is calculated

The tool computes dB = 20 × log₁₀(Vout / Vin). Vout and Vin are voltages in the same unit (volts, millivolts, RMS or peak, as long as both match). Only their ratio matters. The result is in decibels, rounded to two decimals; positive means gain, negative means attenuation, and 0 dB means equal voltages.

Both voltages must be greater than zero because the logarithm of zero or a negative number is undefined; otherwise the tool returns nothing. The factor 20 is for voltage (a field quantity). It assumes both voltages are measured across the same impedance, which is the case when you compare a gain stage or filter. For power ratios the factor would be 10.

Worked example

An amplifier takes in 0.5 V and puts out 2.5 V. The ratio is 2.5 / 0.5 = 5. The base-10 logarithm of 5 is about 0.699. Multiply by 20: 20 × 0.699 ≈ 13.98 dB. If the output were instead 0.25 V for an input of 1 V, the ratio 0.25 would give about −12.04 dB, a loss of signal.

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Common mistakes

  • Using the power formula (10 × log) on voltages. That gives half the correct dB; voltage ratios use 20.
  • Mixing units, such as Vout in millivolts and Vin in volts. The ratio then comes out 1,000 times off, adding 60 dB.
  • Swapping input and output. The sign flips, so a gain of +13.98 dB would show as −13.98 dB.
  • Mixing RMS with peak values. Both voltages should be measured the same way.
  • Entering a negative or zero voltage to represent a phase flip or no signal. The tool needs positive magnitudes and gives no result otherwise.

Sources

About this calculator

This calculator uses the field-quantity decibel formula, dB = 20 × log₁₀(Vout / Vin), which differs from the power-ratio formula (10 × log₁₀) by a factor of two because power is proportional to voltage squared. A ratio of exactly 2 (doubling the voltage) works out to about +6.02 dB, and a ratio of 10 works out to exactly +20 dB.

Audio engineers use it to read gain and attenuation straight off an amplifier's or mixer's voltage figures, electronics designers use it to spec op-amp and filter circuits in datasheets, and it's the same math behind the dB markings on volume knobs and equalizer sliders.

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Comments (1)

  • Editorial team

    A useful reference set for checking the output: doubling the voltage is about +6 dB, ten times is +20 dB, and a voltage of 0.707 times the input is about −3 dB. The half-power point usually quoted as −3 dB is therefore a voltage ratio near 0.71, not 0.5. Note the result is a pure voltage ratio, so it equals power gain only across equal impedances. Are you reading a datasheet or measuring a circuit?

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