Decibel (dB) Calculator

What the decibel calculator does

The decibel expresses a ratio between two quantities on a logarithmic scale, widely used for gain and loss in electronics and audio. This calculator converts a power ratio or a voltage ratio into decibels, handling the logarithm for you.

Below is what a decibel is, the equations behind it, why power and voltage use different factors, and a worked example.

How to use it

1. Enter either a power ratio or a voltage ratio, not both.
2. Use the ratio of the two values, such as output divided by input.
3. Press Calculate for the result in decibels, or Reset to clear it.

What a decibel is

A decibel is a unit for expressing the ratio between two quantities, such as two powers or two voltages, on a logarithmic scale. Rather than saying one signal is a hundred times stronger than another, you can say it is twenty decibels stronger, which is often more convenient. The decibel is not an absolute amount of anything on its own; it always describes a ratio, a comparison between two values. It is used throughout electronics, audio, radio, and acoustics to describe how much a signal is amplified or weakened.

The reason for using a logarithmic unit is that the quantities involved often span an enormous range, from the very faint to the very strong, and a logarithmic scale compresses that range into manageable numbers. It also matches the way human senses respond, since our perception of loudness and brightness is roughly logarithmic, so equal steps in decibels feel like equal changes. A gain expressed in decibels also has a handy property: gains in a chain of stages simply add up rather than multiplying. This calculator converts a ratio into decibels, doing the logarithm automatically.

The equations it uses

For a ratio of two powers, the decibel value is ten times the base-ten logarithm of the ratio:

dB = 10 × log₁₀(P₁ ÷ P₂)

For a ratio of two voltages, the factor is twenty instead of ten:

dB = 20 × log₁₀(V₁ ÷ V₂)

In both cases the logarithm turns the ratio into decibels, with a positive result meaning a gain and a negative result meaning a loss. The calculator takes whichever ratio you provide, applies the right factor, and returns the value in decibels, so you never have to compute a logarithm by hand.

Why power uses ten and voltage uses twenty

A common source of confusion is why power ratios use a factor of ten while voltage ratios use twenty. The answer lies in the relationship between power and voltage. Power is proportional to the square of the voltage, so doubling a voltage quadruples the power. When you express a voltage ratio in decibels, you are really describing the power ratio that goes with it, and squaring the voltage ratio inside the logarithm is the same as doubling the factor in front, turning ten into twenty.

This means the two formulas are consistent, not contradictory: a given ratio of signals comes out to the same number of decibels whether you work from the power or from the voltage, as long as you use the matching factor. The factor of twenty for voltage simply accounts for the squaring that links voltage to power. Keeping this straight is important, because using the wrong factor gives an answer that is off by double. The calculator handles it for you by asking which kind of ratio you are entering and applying the correct factor automatically.

Common decibel values worth knowing

A few decibel values come up so often that they are worth remembering, and they make the scale intuitive. A ratio of three decibels corresponds to roughly doubling the power, while ten decibels is exactly ten times the power. For voltages, six decibels is roughly a doubling, and twenty decibels is ten times the voltage. Zero decibels means the two quantities are equal, a ratio of one, since the logarithm of one is zero.

These landmarks let you estimate decibel values in your head and sense what a figure means. A loss of three decibels has halved the power, which is exactly why the cutoff frequency of a filter, the half-power point, is called the three-decibel point. Each additional ten decibels multiplies the power by another factor of ten, so thirty decibels is a thousand times the power and so on, the scale climbing steeply in real terms while the decibel numbers grow gently. The calculator gives the precise value for any ratio, but these common points provide a useful feel for the results.

Units and precision

The calculator takes either a power ratio or a voltage ratio, as a plain number, and returns the result in decibels. It applies a factor of ten for power ratios and twenty for voltage ratios, with the base-ten logarithm. A ratio greater than one gives a positive decibel value, a gain, while a ratio less than one gives a negative value, a loss. The conversion is exact; entering only one of the two ratio types keeps the calculation unambiguous.

A worked example

Suppose an amplifier increases the power of a signal by a factor of 100.

The gain in decibels is dB = 10 × log₁₀(100) = 10 × 2 = 20 decibels, since the logarithm of 100 is 2. If instead you measured a voltage ratio of 2, the gain would be 20 × log₁₀(2) ≈ 6 decibels, the familiar figure for doubling a voltage. A ratio of exactly 1, meaning no change, would give 0 decibels.

Questions people ask

How do you calculate decibels from a power ratio?

Use dB = 10 × log₁₀(P₁ ÷ P₂). Take the base-ten logarithm of the power ratio and multiply by ten.

How do you calculate decibels from a voltage ratio?

Use dB = 20 × log₁₀(V₁ ÷ V₂). The factor is twenty for voltage because power is proportional to voltage squared.

Why is it ten for power but twenty for voltage?

Because power is proportional to the square of voltage. Squaring the voltage ratio inside the logarithm doubles the factor, turning ten into twenty, so both give the same decibels.

What does three decibels mean?

Roughly a doubling of power, or a halving for minus three decibels. This is why a filter's half-power cutoff is called the three-decibel point.

References

A quick note on where this comes from. The decibel and its logarithmic definition are standard across engineering and acoustics, described by NIST and in Georgia State University's HyperPhysics. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. HyperPhysics, Decibels. http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/db.html
2. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811
3. Wikipedia, Decibel. https://en.wikipedia.org/wiki/Decibel