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Convert voltage ratio to dB

Convert a voltage ratio (V1 / V2) into decibels (dB).

Diagram: Convert voltage ratio to dB
V1
V2
Decibels
—dB
History
Press Enter in any field to keep a snapshot here.

Formula

Formula: dB = 20 × log₁₀(V1 / V2)

Design notes

Use this to express amplifier gain or circuit loss in dB from measured input and output voltages. With V1 = 2 V and V2 = 1 V you get 20 × log₁₀(2) ≈ 6 dB, which you would describe as "6 dB of gain".

It also converts readings taken straight off an oscilloscope or spectrum analyser.

When you need this

For expressing a ratio of two voltages in dB — amplifier gain, attenuation, signal-to-noise ratio, power supply rejection (PSRR) and crosstalk, all of which are specified as voltage ratios.

Voltage ratios use 20·log₁₀

dB = 20 × log₁₀(V1 / V2). The factor is 20, not the 10 used for power.

Put the output, or the larger quantity, on top and the input or reference underneath. A smaller numerator gives a negative result, representing attenuation.

Where it is used

  • Amplifier gain. Output voltage over input voltage. For an inverting stage, Inverting amplifier reports gain and dB together.
  • Signal-to-noise ratio. Signal voltage over noise voltage. Audio work expects 90dB or better (about 31,600 times).
  • PSRR. Supply ripple over the ripple appearing at the output. LDO datasheets quote 60–80dB; 80dB means supply ripple is reduced ten-thousandfold.
  • Crosstalk. Victim voltage over aggressor voltage. −40dB means 1% is leaking across.
  • Shielding effectiveness. Voltage without the shield over voltage with it.

Worked example: checking LDO rejection

  1. A datasheet states PSRR = 70dB at 1kHz.
  2. Convert with dB to ratio: 70dB is about 3,162 times in voltage.
  3. With 100mV of ripple on the input, what remains is 100mV ÷ 3,162 ≈ 32µV.
  4. If the target is under 50µV, that is comfortable. But PSRR varies strongly with frequency, and many LDOs fall to around 20dB by 100kHz.
  5. Following a switching converter, check PSRR at the switching frequency, not at 1kHz.

Frequently asked questions

My result is negative.
The numerator is smaller than the denominator, meaning attenuation. Adopting the convention that the larger quantity goes on top keeps gain positive and loss negative.
When do I use the power form (10·log) instead?
Use 20·log for voltages and 10·log for powers. Where a datasheet simply says "dB", judge from what the parameter measures. Gain, SNR, PSRR and crosstalk are normally voltage ratios; antenna gain and transmit power are power ratios.
Does this require equal impedances?
Strictly, converting to a power ratio assumes the same impedance. But dB as a voltage ratio is defined regardless of impedance, so it is fine for expressing gain or attenuation. Only take care when reinterpreting the figure as power.

Standards and references

  • IEC 60027-3 — Definition of logarithmic quantities.

Last updated: 2026-08-29