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Decibel (dB) Converter

This tool switches between a level and the decibel value that describes it against a reference. Choose a quantity type and a decibel unit, fill in the numbers and press Convert.

What this tool does

The converter moves in two directions: Level to decibels expresses a level as a dB figure, and Decibels to level recovers the level that a dB figure stands for. The quantity type can be Power, Voltage, Current, Frequency or Sound pressure. The decibel unit can be dBm, dBW, dBV, dBmV, dBuV, dBu, dBuA, dBHz, dBSPL or plain dB.

You enter a reference level together with a level, or a reference level together with a decibel value, and press Convert. Nothing is worked out until you press it. The answer appears in cards below the button, Copy puts a result and its unit on the clipboard, and Clear resets the form.

Reading a decibel

A decibel is a logarithmic way of writing a ratio between two levels, using the base 10 logarithm. It names the relationship between the two numbers instead of either one alone, so a very large ratio and a very small one are both written shortly.

Each result also shows the plain ratio. Setting the quantity type to Power with a reference level of 5 and a level of 10 gives Decibels: 3.01029995663981 dB; Ratio: 2 — a level that is twice its reference.

Decibel formula

Level to decibels for power: Decibels = 10 × log10(Level / Reference level). The worked case 10 × log10(10 / 5) ≈ 3.01029995663981 dB is exactly that.

Level to decibels for voltage, current and sound pressure: Decibels = 20 × log10(Level / Reference level), which is how 20 × log10(100 / 1) = 40 dBV comes about.

Decibels to level multiplies the reference instead of taking a logarithm: 5 × 10^(6 / 20) ≈ 9.9763115748444 V, the case reported as Level: 9.9763115748444 V; Ratio: 1.99526231496888. For power the exponent is divided by 10 rather than by 20.

In the examples with a reference level of 1, the expressions evaluate directly: 10 × log10(2 / 1) ≈ 3.01029995663981 dBm, 10 × log10(1000 / 1) = 30 dBm and 10 × log10(10 / 1) = 10 dBW.

How exact the numbers are

Figures such as 3.01029995663981 dB and 9.9763115748444 V come straight out of the logarithm and are shown in full. Other cases are exact rather than rounded, for instance Decibels: 30 dBm; Ratio: 1000, Decibels: 10 dBW; Ratio: 10 and Decibels: 40 dBV; Ratio: 100.