Electronics Signal Tool

dB Calculator

Calculate decibel gain, attenuation and ratios for voltage, current and power. Use the correct 10 log₁₀ power relationship or 20 log₁₀ voltage/current relationship for electronics, audio, RF and signal analysis.

Decibel Calculator

Calculate dB from a ratio or calculate the ratio represented by a dB value.

Pout / Pin
Vout / Vin or Iout / Iin
dB gain (+) or attenuation (-)
Power Ratio Result
+3.0103 dB
A 2× power ratio corresponds to approximately +3.01 dB.
Power Ratio 2×
Voltage / Current Ratio 2×
dB Result +3.0103 dB
Linear Interpretation 2× power

dB = 10 × log₁₀(Pout / Pin)

dB Calculation Formulas

The decibel is a logarithmic way of expressing a ratio. The correct equation depends on whether the ratio represents power or an amplitude quantity such as voltage or current.

Power Ratio

dB = 10 log₁₀(Pout / Pin)

Use this formula when comparing two power levels. Pout is the output power and Pin is the input power.

  • 2× power ≈ +3.01 dB
  • 10× power = +10 dB
  • 100× power = +20 dB
  • 0.5× power ≈ -3.01 dB

Voltage Ratio

dB = 20 log₁₀(Vout / Vin)

The 20 log₁₀ expression is used for voltage ratios when the impedance conditions make the voltage-to-power relationship applicable.

  • 2× voltage ≈ +6.02 dB
  • 10× voltage = +20 dB
  • 0.5× voltage ≈ -6.02 dB
  • 1× voltage = 0 dB

Reverse Conversion

R = 10^(dB/10)

For power ratios, convert dB back to a linear ratio using 10 raised to the dB value divided by 10.

R = 10^(dB/20)

For voltage or current ratios, use 20 in the denominator.

Important: Do not use 10 log₁₀ for a voltage ratio simply because the quantities are electrical. Voltage and current ratios normally use 20 log₁₀ when expressed as amplitude ratios under the appropriate impedance conditions. Power ratios use 10 log₁₀.

Common dB Values

These reference values show the difference between power ratios and voltage/current ratios.

dB Power Ratio Voltage / Current Ratio Interpretation
-20 dB 0.01× 0.1× Strong attenuation
-10 dB 0.1× 0.3162× 10× lower power
-6.02 dB 0.25× 0.5× Half voltage/current
-3.01 dB 0.5× 0.7079× Half power
0 dB 1× 1× Equal ratio
3.01 dB 2× 1.4125× Approximately double power
6.02 dB 4× 2× Double voltage/current
10 dB 10× 3.1623× 10× power
20 dB 100× 10× 100× power

How the dB Calculator Works

Choose the Ratio Type

Select power ratio when comparing input and output power, or voltage/current when comparing amplitude quantities.

Enter the Ratio

Enter a positive linear ratio such as 0.5, 1, 2 or 10. The calculator applies the appropriate logarithmic formula.

Read the dB Value

Positive values represent gain, zero represents an equal ratio, and negative values represent attenuation or loss.

Worked dB Examples

Example 1: Power Gain

An amplifier increases power from 1 W to 2 W. Calculate the gain in dB.

dB = 10 log₁₀(2 / 1)
dB ≈ +3.01 dB

The amplifier provides approximately 3.01 dB of power gain.

Example 2: Power Loss

A circuit passes 50% of the input power.

dB = 10 log₁₀(0.5)
dB ≈ -3.01 dB

A power ratio of 0.5 corresponds to approximately -3.01 dB.

Example 3: Voltage Gain

A circuit increases voltage from 1 V to 2 V under suitable impedance conditions.

dB = 20 log₁₀(2 / 1)
dB ≈ +6.02 dB

The voltage gain is approximately +6.02 dB.

Example 4: -20 dB Attenuation

Find the power ratio corresponding to -20 dB.

Pout / Pin = 10^(-20/10)
Pout / Pin = 0.01

Therefore, -20 dB corresponds to 1% of the original power, or a 100:1 reduction.

dB Calculator Applications

Decibels are widely used because logarithmic ratios make very large signal ranges easier to describe and compare.

RF & Wireless

Calculate antenna gain, cable loss, amplifier gain, filter attenuation and other RF signal ratios.

Audio

Express amplifier gain, attenuator settings, signal levels and frequency-response changes.

Filters

Analyze insertion loss, attenuation and gain when evaluating filters and signal-conditioning circuits.

Communications

Compare signal gain and loss through transmission paths, amplifiers, cables and other components.

Practical dB Notes

Positive dB

A positive dB value indicates that the output is greater than the input for the ratio being calculated. It represents gain.

Negative dB

A negative dB value indicates that the output is smaller than the input. It represents attenuation or loss.

0 dB

Zero dB means the ratio is exactly 1. It does not necessarily mean zero voltage or zero power; it means equal input and output quantities.

Impedance matters: The voltage-ratio formula 20 log₁₀(Vout/Vin) corresponds directly to a power ratio when the relevant input and output impedances are equal. If impedances differ, calculate power explicitly or account for the impedance difference rather than assuming the voltage ratio alone represents the power ratio.

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dB Calculator FAQ

For a power ratio, use dB = 10 × log10(Pout / Pin). A ratio greater than 1 produces positive dB gain, while a ratio less than 1 produces negative dB loss.

For voltage or current ratios under the same impedance conditions, use dB = 20 × log10(Vout / Vin).

Voltage is related to power through a squared relationship when impedance is constant. Because P is proportional to V², the power expression 10 log10 becomes 20 log10 for voltage ratios.

A value of 0 dB means the output-to-input ratio is 1. For voltage, current or power, the output equals the input under the conditions represented by the calculation.

A negative dB value represents attenuation or loss. For example, a voltage ratio of 0.5 corresponds to approximately -6.02 dB.

A +3 dB power ratio is approximately 2:1. Conversely, -3 dB corresponds to approximately half the power.

A voltage ratio of approximately 2:1 corresponds to +6.02 dB when the impedance conditions are appropriate for using the voltage-ratio formula.

Yes. For power, ratio = 10^(dB/10). For voltage or current, ratio = 10^(dB/20), assuming the appropriate impedance conditions.