# 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
*Convert*button:

### 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} = 10* *log_{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} = 20* *log_{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 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 | 10^{5} |
10^{10} |