Decibel (dB) Calculator

FAQ

What is a decibel (dB)?

A decibel is a logarithmic unit used to express the ratio between two values, commonly power or voltage. Because it uses a logarithmic scale, decibels can represent very large or very small ratios with manageable numbers. For example, a 1,000,000:1 power ratio is simply 60 dB.

What is the difference between power dB and voltage dB?

Power dB uses the formula dB = 10 × log₁₀(P₂/P₁), while voltage dB uses dB = 20 × log₁₀(V₂/V₁). The factor of 20 for voltage accounts for the squared relationship between power and voltage (P ∝ V²). Both yield the same dB result for equivalent systems.

What is dBm and how does it differ from dBW?

dBm is decibels relative to 1 milliwatt, and dBW is decibels relative to 1 watt. Since 1 watt = 1000 milliwatts, dBW = dBm − 30. For example, 0 dBm = 1 mW = −30 dBW, and 30 dBm = 1 W = 0 dBW.

What does 3 dB mean?

A 3 dB increase represents approximately doubling the power (ratio of about 2). A 3 dB decrease means halving the power. This is known as the "3 dB rule" and is one of the most important reference points in electronics. For voltage, 3 dB corresponds to a factor of about 1.414.

How do I add two decibel levels together?

Decibels do not add arithmetically. Convert each level to intensity with 10^(L/10), add the intensities and convert back with 10 × log10 of the sum. Two equal 80 dB sources give 83 dB, not 160 dB, and ten equal sources add 10 dB. Choose Add dB Levels, enter the levels separated by commas, and optionally a background level to subtract.

How does sound level change with distance?

From a point source, the level falls by 20 × log10(r2/r1): about 6 dB every time the distance doubles (the inverse square law). From a line source such as a busy road it falls by about 3 dB per doubling. Choose dB vs Distance and enter the level measured at one distance to get it at another.

What are dBu and dBV?

Both express an audio voltage in decibels. dBV is relative to 1 volt RMS; dBu is relative to 0.775 volt RMS, the voltage that gives 1 mW into 600 ohms. Professional +4 dBu line level is 1.228 V and consumer −10 dBV is 0.316 V, about 11.8 dB apart.

How do I convert dB back to a linear ratio?

For power ratio: ratio = 10^(dB/10). For voltage ratio: ratio = 10^(dB/20). For example, 20 dB = 100× power ratio or 10× voltage ratio.

How much dB gain is needed to increase an amplifier from 1 watt to 10 watts?

A tenfold power increase is 10 dB, because power gain in decibels is 10 × log10(output power ÷ input power). For 10 W out and 1 W in, that is 10 × log10(10), or 10 dB. This describes the ratio between the two power levels; it does not mean the output is 10 dBm, since dBm is an absolute level referenced to 1 milliwatt.

What is +20 dBm in milliwatts?

+20 dBm equals 100 milliwatts. The conversion is power in milliwatts = 10 raised to the dBm value divided by 10, so 10^(20/10) = 100. A useful reference is 0 dBm = 1 mW and +10 dBm = 10 mW. Remember that dBm is an absolute power level, while a value such as 20 dB describes a ratio or gain.

When can I use the voltage dB formula without knowing the circuit impedance?

The voltage formula, 20 × log10(V2/V1), gives the same dB difference as the power formula when both voltages are measured across the same impedance. If the impedances differ, voltage ratio alone may not represent the power ratio. For example, doubling voltage across an unchanged resistance means four times the power, or about 6 dB. For different loads, compare power directly or include impedance.