What is a decibel (dB)?

Decibel (dB) definition, how to convert, calculator and dB to ratio 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 P1 and P0:

RatioB = log10(P1 / P0)

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 P1 and P0:

RatiodB = 10·log10(P1 / P0)

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 V1 and V0:

RatiodB = 10·log10(V12 / V02) = 20·log10(V1 / V0)

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.

  1. Set the quantity type and decibel unit.
  2. Enter the values in one or two of the text boxes and press the corresponding Convert button:
           
  Quantity type:      
  Decibel unit:      
  Reference level:    
  Level:  
  Decibels:  
         
           

Power ratio to dB conversion

The gain GdB is equal to 10 times base 10 logarithm of the ratio of the power P2 and the reference power P1.

GdB = 10 log10(P2 / P1)

 

P2 is the power level.

P1 is the referenced power level.

GdB 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.

GdB = 10 log10(Pout/ Pin) = 10 log10(10W/5W) = 3.01dB

dB to power ratio conversion

The power P2 is equal to the reference power P1 times 10 raised by the gain in GdB divided by 10.

P2 = P1  · 10(GdB / 10)

 

P2 is the power level.

P1 is the referenced power level.

GdB is the power ratio or gain in dB.

Amplitude ratio to dB conversion

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

GdB = 20 log10(A2 / A1)

 

A2 is the amplitude level.

A1 is the referenced amplitude level.

GdB is the amplitude ratio or gain in dB.

dB to amplitude ratio conversion

A2 = A1  · 10(GdB / 20)

A2 is the amplitude level.

A1 is the referenced amplitude level.

GdB 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.

Vout = Vin · 10 (GdB / 20) = 5V · 10 (6dB / 20) = 9.976V ≈ 10V

Voltage gain

The voltage gain (GdB) is 20 times the base 10 logarithm of the ratio of the output voltage (Vout) and the input voltage (Vin):

GdB = 20·log10(Vout / Vin)

Current gain

The current gain (GdB) is 20 times the base 10 logarithm of the ratio of the output current (Iout) and the input current (Iin):

GdB = 20·log10(Iout / Iin)

Acoustic gain

The acoustic gain of a hearing aid (GdB) is 20 times the base 10 logarithm of the ratio of the output sound level (Lout) and the input sound level (Lin).

GdB = 20·log10(Lout / Lin)

Signal to Noise Ratio (SNR)

The signal to noise ratio (SNRdB) is 20 times the base 10 logarithm of the signal amplitude (Asignal) and the noise amplitude (Anoise):

SNRdB = 20·log10(Asignal / Anoise)

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 1μVRMS voltage amplitude ratio
dBmV decibel millivolt 1mVRMS voltage amplitude ratio
dBV decibel volt 1VRMS voltage amplitude ratio
dBu decibel unloaded 0.775VRMS voltage amplitude ratio
dBZ decibel Z 1μm3 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 meter or SPL meter is 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 105 1010

 

dBm unit ►

 


See also

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