## What is a decibel (dB)?

Decibel (dB) definition, how to convert, calculator and dB to ratio table.

- Decibel (dB) definition
- Decibels to watts, volts, hertz, pascal calculator
- Power ratio to dB conversion
- dB to power ratio conversion
- Amplitude ratio to dB conversion
- dB to amplitude ratio conversion
- Absolute decibel units
- Relative decibel units
- Sound level meter
- dB-SPL table
- dB to ratio conversion table
## Decibel (dB) definition

Decibel (Symbol: dB) is a logarithmic unit that indicates ratio or gain.

Decibel is used to indicate the level of acoustic waves and electronic signals.

The logarithmic scale can describe very big or very small numbers with shorter notation.

The dB level can be viewed as relative gain of one level vs. other level, or absolute logarithmic scale level for well known reference levels.

Decibel is a dimensionless unit.

The ratio in bels is the base 10 logarithm of the ratio of P

_{1}and P_{0}:

Ratio_{B}= log_{10}(P_{1}/P_{0})Decibel is one tenth of a bel, so 1 bel is equal to 10 decibel:

1B = 10dB

## Power ratio

The power ratio in decibels (dB) is 10 times base 10 logarithm of the ratio of P

_{1}and P_{0}:

Ratio_{dB}= 10·log_{10}(P_{1}/P_{0})## Amplitude ratio

The ratio of quantities like voltage, current and sound pressure level are calculated as ratio of squares.

The amplitude ratio in decibels (dB) is 20 times base 10 logarithm of the ratio of V

_{1}and V_{0}:

Ratio_{dB}= 10·log_{10}(V_{1}^{2}/V_{0}^{2}) = 20·log_{10}(V_{1}/V_{0})## Decibels to watts, volts, hertz, pascal conversion calculator

Convert dB, dBm, dBW, dBV, dBmV, dBμV, dBu, dBμA, dBHz, dBSPL, dBA to watts, volts, ampers, hertz, sound pressure.

- Set the quantity type and decibel unit.
- Enter the values in one or two of the text boxes and press the corresponding
Convertbutton:## Power ratio to dB conversion

The gain G

_{dB}is equal to 10 times base 10 logarithm of the ratio of the power P_{2}and the_{ }reference power P_{1}.

G_{dB}= 10log_{10}(P_{2}/P_{1})

P

_{2}is the power level.P

_{1}is the referenced power level.G

_{dB}is the power ratio or gain in dB.

## Example

Find the gain in dB for a system with input power of 5W and output power of 10W.

G_{dB}= 10 log_{10}(P/_{out}P) = 10 log_{in}_{10}(10W/5W) = 3.01dB## dB to power ratio conversion

The power P

_{2}is equal to the reference power P_{1}times 10 raised by the gain in G_{dB}divided by 10.

P_{2}=P_{1}_{ }·10^{(G}dB^{ / 10)}

P

_{2}is the power level.P

_{1}is the referenced power level.G

_{dB}is the power ratio or gain in dB.## Amplitude ratio to dB conversion

For amplitude of waves like voltage, current and sound pressure level:

G_{dB}= 20log_{10}(A_{2}/A_{1})

A

_{2}is the amplitude level.A

_{1}is the referenced amplitude level.G

_{dB}is the amplitude ratio or gain in dB.## dB to amplitude ratio conversion

A_{2}=A_{1}10_{ }·^{(G}dB^{ / 20)}A

_{2}is the amplitude level.A

_{1}is the referenced amplitude level.G

_{dB}is the amplitude ratio or gain in dB.

## Example

Find the output voltage for a system with input voltage of 5V and voltage gain of 6dB.

V=_{out}V_{in}·10^{(G}dB^{ / 20)}= 5V·10^{(6dB / 20)}= 9.976V ≈ 10V## Voltage gain

The voltage gain (

G_{dB}) is 20 times the base 10 logarithm of the ratio of the output voltage (V_{out}) and the input voltage (V_{in}):

G_{dB}= 20·log_{10}(V_{out}/V_{in})## Current gain

The current gain (

G_{dB}) is 20 times the base 10 logarithm of the ratio of the output current (I_{out}) and the input current (I_{in}):

G_{dB}= 20·log_{10}(I_{out}/I_{in})## Acoustic gain

The acoustic gain of a hearing aid (

G_{dB}) is 20 times the base 10 logarithm of the ratio of the output sound level (L_{out}) and the input sound level (L_{in}).

G_{dB}= 20·log_{10}(L_{out}/L_{in})## Signal to Noise Ratio (SNR)

The signal to noise ratio (

SNR_{dB}) is 20 times the base 10 logarithm of the signal amplitude (A_{signal}) and the noise amplitude (A_{noise}):

SNR_{dB}= 20·log_{10}(A_{signal}/A_{noise})## Absolute decibel units

Absolute decibel units are referenced to specific magnitude of measurement unit:

Unit Name Reference Quantity Ratio dBm decibel milliwatt 1mW electric power power ratio dBW decibel watt 1W electric power power ratio dBrn decibel reference noise 1pW electric power power ratio dBμV decibel microvolt 1μV _{RMS}voltage amplitude ratio dBmV decibel millivolt 1mV _{RMS}voltage amplitude ratio dBV decibel volt 1V _{RMS}voltage amplitude ratio dBu decibel unloaded 0.775V _{RMS}voltage amplitude ratio dBZ decibel Z 1μm ^{3}reflectivity amplitude ratio dBμA decibel microampere 1μA current amplitude ratio dBohm decibel ohms 1Ω resistance amplitude ratio dBHz decibel hertz 1Hz frequency power ratio dBSPL decibel sound pressure level 20μPa sound pressure amplitude ratio dBA decibel A-weighted 20μPa sound pressure amplitude ratio ## Relative decibel units

Unit Name Reference Quantity Ratio dB decibel - - power/field dBc decibel carrier carrier power electric power power ratio dBi decibel isotropic isotropic antenna power density power density power ratio dBFS decibel full scale full digital scale voltage amplitude ratio dBrn decibel reference noise ## Sound level meter

Sound level meterorSPL meteris a device that measures the sound pressure level (SPL) of sound waves in decibels (dB-SPL) units.SPL meter is used to test and measure the loudness of the sound waves and for noise pollution monitoring.

The unit for measuring of sound pressure level is pascal (Pa) and in logarithmic scale the dB-SPL is used.

## dB-SPL table

Table of common sound pressure levels in dBSPL:

Sound type Sound level (dB-SPL) Hearing threshold 0 dBSPL Whisper 30 dBSPL Air conditioner 50-70 dBSPL Conversation 50-70 dBSPL Traffic 60-85 dBSPL Loud music 90-110 dBSPL Airplane 120-140 dBSPL ## dB to ratio conversion table

dB Amplitude ratio Power ratio -100 dB 10 ^{-5}10 ^{-10}-50 dB 0.00316 0.00001 -40 dB 0.010 0.0001 -30 dB 0.032 0.001 -20 dB 0.100 0.010 -10 dB 0.316 0.100 -6 dB 0.501 0.251 -3 dB 0.708 0.501 -2 dB 0.794 0.631 -1 dB 0.891 0.794 0 dB 1.000 1.000 1 dB 1.122 1.259 2 dB 1.259 1.585 3 dB 1.413 2 ≈ 1.995 6 dB 2 ≈ 1.995 3.981 10 dB 3.162 10.000 20 dB 10.000 100.000 30 dB 31.623 1000.000 40 dB 100.000 10000.000 50 dB 316.228 100000.000 100 dB 10 ^{5}10 ^{10}

## See also