Decibel Calculator

Calculate decibel values for power and voltage ratios. Convert dB to linear ratios and watts to dBm.

Decibel Calculator tool

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Example

Input: Power ratio to dB: 2 W compared with a 1 W reference

Result: 3.0103 dB

dB = 10 x log10(2 / 1) = 10 x 0.30103 = 3.0103 dB, which is why doubling power is called +3 dB.

Ratios in Decibels

RatioPower (10 log)Voltage (20 log)
0.5-3.01 dB-6.02 dB
10 dB0 dB
23.01 dB6.02 dB
34.77 dB9.54 dB
46.02 dB12.04 dB
1010 dB20 dB
10020 dB40 dB
100030 dB60 dB
  1. Select the conversion mode - power or voltage ratio to dB, dB back to a power or voltage ratio, or watts to and from dBm.
  2. For ratio to dB modes, enter the measured value as Value 1 and the reference value as Value 2 (for example, output and input power).
  3. For dB to ratio modes, enter the dB value as Value 1 and the reference as Value 2 (use 1 to get a pure ratio).
  4. For dBm conversions, enter the power in watts or the level in dBm as Value 1 - the reference field is not used.
  5. Review the result along with the exact formula used, and copy either one with its copy button.

Decibels, Power Ratios and dBm

A decibel (dB) compares two levels on a log scale. For power, dB = 10 x log10(P1 / P2), so doubling the power adds about 3 dB and ten times the power adds 10 dB. For voltage or sound pressure, the factor is 20: dB = 20 x log10(V1 / V2), so doubling a voltage adds about 6 dB.

Why two formulas? Power goes up with the square of voltage. A voltage ratio of 2 is a power ratio of 4, and both come out to 6 dB. Use the power modes for watts and the voltage modes for volts, amps or sound pressure. Mixing them up is the most common mistake, and it gives an answer that is off by a factor of two in dB.

The calculator has six modes. You can turn a power or voltage ratio into dB, turn dB back into a ratio, or convert between watts and dBm. For ratios, Value 1 is the level you measured and Value 2 is the reference. Set the reference to 1 to get a pure ratio. dBm is power compared with 1 milliwatt, so 0 dBm is 1 mW and 30 dBm is 1 W. The reference field is not used in the dBm modes. Every result shows the formula with your numbers in it.

Decibels make gains and losses easy to add up. An amplifier with 20 dB gain after a cable with 3 dB loss gives 17 dB overall. That is why radio link budgets and audio gain staging use them. For the logarithm math itself, try the Logarithm Calculator. For radio wavelengths, see the Frequency and Wavelength Converter.

Formula / How It Works

dB (power) = 10 x log10(P1/P2) | dB (voltage) = 20 x log10(V1/V2) | dBm = 10 x log10(P / 0.001) | P (W) = 0.001 x 10^(dBm / 10)

Frequently Asked Questions

Because 10 x log10(2) = 3.01. Every doubling of power adds about 3 dB, and every halving takes away about 3 dB. So a 100 W amplifier is only 3 dB louder than a 50 W one. To sound twice as loud to the ear, you need about 10 dB more, which is ten times the power.
Use 10 x log10 for power quantities, such as watts or sound intensity. Use 20 x log10 for field quantities, such as voltage, current or sound pressure. Power goes up with the square of voltage, and the 20 accounts for that square. Both give the same dB for the same change.
Use P = 0.001 x 10^(dBm / 10). So 0 dBm is 1 mW, 20 dBm is 100 mW and 30 dBm is 1 W. Each 10 dBm step is ten times the power. Negative values are fractions of a milliwatt. For example, -30 dBm is 1 microwatt.
dB is a ratio between two levels and has no unit on its own. dBm is an absolute power level, measured against 1 milliwatt. You can add dB to dBm: a 10 dBm signal through a 20 dB amplifier comes out at 30 dBm, which is 1 W.

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