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Decibel Gain/Ratio Converter

Science

Convert decibels (dB) to linear power ratio or voltage/amplitude ratio, and back — for audio, RF, and electronics gain and attenuation calculations.

Reviewed by the thecalcu.com team · Last updated July 26, 2026

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What is a dB Gain?

A Decibel Gain/Ratio Converter translates between decibels (dB) and the linear power or voltage ratios they represent, the core calculation behind amplifier gain, cable attenuation, and signal-to-noise measurements in audio and RF electronics. Because a decibel is a logarithmic unit, small dB numbers correspond to surprisingly large or small linear ratios: a 20 dB gain means a hundredfold increase in power, while -3 dB means the power has roughly halved.

This converter handles both conventions used across electronics: the 10×log10 formula for power ratios, and the 20×log10 formula for voltage or amplitude ratios. It's distinct from the Sound Converter, which is scoped to acoustic sound-pressure-level measurements (dB SPL relative to the human hearing threshold) rather than electrical signal gain.

Why Use a Decibel Gain/Ratio Converter?

Amplifier datasheets, RF link budgets, and audio equipment specifications express gain and loss in decibels, but the actual physical effect, how much stronger or weaker a signal actually becomes, is only clear once converted to a linear ratio. Manually applying the correct logarithmic formula, and remembering whether to use the factor of 10 or 20, is a common source of errors.

Two concrete situations this solves: converting an amplifier's advertised +26 dB gain spec into an actual power multiplication factor to check if it matches your circuit's power budget, and converting a cable's -3 dB attenuation rating into a voltage ratio to estimate signal loss over a long cable run.

Who Should Use This Converter?

  • Audio engineers converting amplifier or mixer gain specifications between dB and linear power/voltage ratios for gain-staging calculations.
  • RF and electronics engineers working with link budgets, antenna gain, or attenuator specifications that mix dB and linear units.
  • Electronics hobbyists and students learning the relationship between decibels and the physical power or voltage changes they represent.
  • Home theatre and hi-fi enthusiasts interpreting speaker sensitivity and amplifier gain specs that use dB notation.
  • Telecom and networking professionals evaluating cable, connector, or splitter loss specified in dB, alongside the Electric Potential Converter for voltage-related calculations.

What Insights Does the dB Gain Converter Give You?

Converting dB to Power Ratio shows how many times greater (or smaller) the output power is compared to the input, essential for power budget calculations in amplifier and RF chain design. Converting dB to Voltage/Amplitude Ratio shows the equivalent multiplication factor for voltage or signal amplitude, which is the number that matters for audio signal levels and oscilloscope measurements.

Because the two ratio types use different formulas (10-log vs 20-log), the same dB value produces two different linear numbers depending on which type you select, this converter makes that distinction explicit rather than leaving you to remember which formula applies to your situation.

How to use this dB Gain calculator

  1. Select your starting unit from the From dropdown, dB, Power Ratio, or Voltage/Amplitude Ratio.
  2. Enter the value you want to convert, such as 20 for a 20 dB gain spec.
  3. Select your target unit from the To dropdown, such as Power Ratio (linear, P₂/P₁).
  4. Read the converted result, which updates instantly.
  5. Use the swap (⇅) button to reverse the conversion direction, for example, going from a known power ratio back to dB.
  6. If working with voltage/amplitude measurements rather than power, make sure to select the Voltage/Amplitude Ratio unit instead of Power Ratio, since they produce different linear values for the same dB figure.

Formula & Methodology

All conversions route through dB as the canonical unit:

dB = 10 × log₁₀(Power Ratio)  |  Power Ratio = 10^(dB ÷ 10)
dB = 20 × log₁₀(Voltage Ratio)  |  Voltage Ratio = 10^(dB ÷ 20)

Worked example: Converting 20 dB to a power ratio, Power Ratio = 10^(20÷10) = 10² = 100, meaning the output power is 100 times the input. Converting that same 20 dB to a voltage ratio instead gives 10^(20÷20) = 10¹ = 10, meaning the output voltage is 10 times the input, illustrating why the two ratio types diverge even for an identical dB value.

Frequently Asked Questions

A decibel is a logarithmic unit used to express the ratio between two power or amplitude levels, such as an amplifier's output versus input, or a signal's strength before and after passing through a cable. It compresses ratios that can span many orders of magnitude (like a millionfold power increase) into small, easy-to-read numbers.
Power ratio = 10^(dB ÷ 10), which is the inverse of dB = 10 × log10(power ratio). This converter applies that formula directly, for example, +3 dB converts to a power ratio of approximately 2, meaning the power has roughly doubled.
Power ratios use the formula dB = 10 × log10(P₂/P₁), while voltage or amplitude ratios use dB = 20 × log10(V₂/V₁), the factor of 20 instead of 10 accounts for power being proportional to voltage squared. Importantly, both formulas give the same dB number for the same underlying physical change in a matched-impedance system, but the linear ratio itself differs: a 6 dB change means a power ratio of about 4 but a voltage ratio of about 2.
Select dB as your From unit and either Power Ratio or Voltage/Amplitude Ratio as your To unit, depending on which quantity you're working with. Enter your dB value and the tool applies the correct 10-log or 20-log formula automatically.
Because power ratio = 10^(dB/10), a 3 dB increase gives 10^0.3 ≈ 2 (double power), while voltage ratio = 10^(dB/20), so a 3 dB increase only gives about 1.41× voltage, it takes 6 dB (10^(6/20) ≈ 2) to double voltage. This is a common source of confusion in audio and RF engineering, and this converter makes the distinction explicit by offering both ratio types.
A negative dB value represents attenuation or loss rather than gain, for example, -10 dB means the power ratio is 0.1 (a 90% reduction), which is common when describing cable loss, filter attenuation, or a quiet audio signal relative to a reference level. This converter handles negative dB values the same way as positive ones, applying the same logarithmic formulas.
Consumer audio amplifiers commonly specify gain between 20 dB and 40 dB, which corresponds to power ratios of 100 to 10,000 times using this converter's Power Ratio conversion. Professional RF amplifiers can specify gain up to 60 dB or more for signal boosting applications.
0 dB always corresponds to a ratio of exactly 1, meaning no change in power or voltage, the output equals the input. This is the reference point the entire dB scale is built around, whether you're measuring gain (positive dB) or loss (negative dB).
No, dBm and dBW are absolute power units referenced to a fixed value (1 milliwatt or 1 watt respectively), while this converter works with relative dB values expressing a ratio between two power or voltage levels, such as an amplifier's gain. To convert dBm to watts, you would additionally need to apply the 1 mW reference, which this general-purpose ratio converter does not assume.
The [Sound Converter](/sound-converter/) is scoped to acoustic sound pressure level units (dB SPL, Pascal, micropascal), which measure physical sound pressure relative to the standard hearing threshold reference. This Decibel Gain/Ratio Converter is scoped to electrical and RF signal gain, the ratio between two power or voltage levels in a circuit, amplifier, or cable, a related but distinct application of the decibel unit.
Also known as
db to power ratiodb to voltage ratiodecibel gain calculatorpower ratio to dbamplifier gain converterdb attenuation converter