# What is a decibel?

Unlike other units of measurement, such as the Volt, dB is not an absolute measure. Rather, dB expressed how much bigger ( or smaller ) one this is when compared to another.

## What is a logarithm?

ratio | power of ten | logarithm |
---|---|---|

.000001 | $10^{-6}$ | $\log ( .000001 ) = -6$ |

.00001 | $10^{-5}$ | $\log ( .00001 ) = -5$ |

.0001 | $10^{-4}$ | $\log ( .0001 ) = -4$ |

.001 | $10^{-3}$ | $\log ( .001 ) = -3$ |

.01 | $10^{-2}$ | $\log ( .01 ) = -2$ |

.1 | $10^{-1}$ | $\log ( .1 ) = -1$ |

1 | $10^{0}$ | $\log ( 1 ) = 0$ |

10 | $10^{1}$ | $\log ( 10 ) = 1$ |

100 | $10^{2}$ | $\log ( 100 ) = 2$ |

1,000 | $10^{3}$ | $\log ( 1,000 ) = 3$ |

10,000 | $10^{4}$ | $\log ( 10,000 ) = 4$ |

100,000 | $10^{5}$ | $\log ( 100,000 ) = 5$ |

1,000,000 | $10^{6}$ | $\log ( 1,000,000 ) = 6$ |

## dB for voltages

for 2 voltages, dB = **$20 * \log{ V_1 / V_2 }$**

voltage ratio | power of ten | logarithm | dB |
---|---|---|---|

.000001 | $10^{-6}$ | $\log ( .000001 ) = -6$ | -120dB |

.00001 | $10^{-5}$ | $\log ( .00001 ) = -5$ | -100dB |

.0001 | $10^{-4}$ | $\log ( .0001 ) = -4$ | -80dB |

.001 | $10^{-3}$ | $\log ( .001 ) = -3$ | -60dB |

.01 | $10^{-2}$ | $\log ( .01 ) = -2$ | -40dB |

.1 | $10^{-1}$ | $\log ( .1 ) = -1$ | -20dB |

1 | $10^{0}$ | $\log ( 1 ) = 0$ | 0dB |

10 | $10^{1}$ | $\log ( 10 ) = 1$ | 20dB |

100 | $10^{2}$ | $\log ( 100 ) = 2$ | 40dB |

1,000 | $10^{3}$ | $\log ( 1,000 ) = 3$ | 60dB |

10,000 | $10^{4}$ | $\log ( 10,000 ) = 4$ | 80dB |

100,000 | $10^{5}$ | $\log ( 100,000 ) = 5$ | 100dB |

1,000,000 | $10^{6}$ | $\log ( 1,000,000 ) = 6$ | 120dB |

## dB for power

for power, dB = **$10 * \log{ P_1 / P_2 }$**

power ratio | power of ten | logarithm | dB |
---|---|---|---|

.000001 | $10^{-6}$ | $\log ( .000001 ) = -6$ | -60dB |

.00001 | $10^{-5}$ | $\log ( .00001 ) = -5$ | -50dB |

.0001 | $10^{-4}$ | $\log ( .0001 ) = -4$ | -40dB |

.001 | $10^{-3}$ | $\log ( .001 ) = -3$ | -30dB |

.01 | $10^{-2}$ | $\log ( .01 ) = -2$ | -20dB |

.1 | $10^{-1}$ | $\log ( .1 ) = -1$ | -10dB |

1 | $10^{0}$ | $\log ( 1 ) = 0$ | 0dB |

10 | $10^{1}$ | $\log ( 10 ) = 1$ | 10dB |

100 | $10^{2}$ | $\log ( 100 ) = 2$ | 20dB |

1,000 | $10^{3}$ | $\log ( 1,000 ) = 3$ | 30dB |

10,000 | $10^{4}$ | $\log ( 10,000 ) = 4$ | 40dB |

100,000 | $10^{5}$ | $\log ( 100,000 ) = 5$ | 50dB |

1,000,000 | $10^{6}$ | $\log ( 1,000,000 ) = 6$ | 60dB |

## Some specific absolute dB measures

Abbreviation | What is Measured | Reference Value | Notes |
---|---|---|---|

dBW | power | 1 Watt | not seen that much |

dBm | power | 1 milliwatt | this is more common |

dBV | voltage | 1 Volt | not used that much |

dBu | voltage | .775 Volts | aka dBv — why .775 Volts?? see below? |

dBmV | voltage | 1mV = .001 Volts | |

dbSPL | sound pressure | 'quietest sound ear can hear' |

## Some examples, and typical signal levels

This link to an online dB calculator, will be helpful in the following examples: calculator

### Example: Consumer and Professional Line Level

If dB hasn't been confusing enough, the fact that 'line-level' can mean multiple things really puts the icing on the cake. There is perhaps more confusion about this than just about everything. If you understand the following, you should be able to stump quite a few folks in the world of audio.

First off, remember that when using dB for an absolute measure, we need to always be clear on what our reference is. Remember that dBV is dB, relative to 1 Volt, and dBu is dB relative to .775 Volts.

First we will look at converting between dBV and dBu. From the calculator, we see that 0dBu is -2.2dBV and that 0dBV is +2.2dBu — so to convert from dBu to dBV, we need to subtract 2.2 — alternatively, to convert from dbV to dBu, we need to add 2.2.

Here is the deal: *Consumer* line-level is expressed as -10**dBV** and Professional line level is +4**dBu**. Very often, you will here someone say that Consumer level is 14dB lower than Pro line-level. In doing this simple math, it is easy to forget that you first need to make sure that both measurements are using the same reference. In this example, we will convert everything to dBu and then determine what the real difference is.

-10dBV = (-10 + 2.2)dBu = -7.8dBu.

The difference between +4dBu and -7.8dBu is +4 - (-7.8) = +4 + 7.8 = 11.8dB, which is the real difference between consumer line level and professional line level.

### Example: Sound Pressure Level ( SPL )

Example Sound | Typical dBSPL | Pressure in 'Pascals' (Pa) |
---|---|---|

threshold of hearing | 0 | .00002 |

rustling leaves | 20 | .0002 |

normal conversation | 60 | .02 |

outboard motor | 80 | .2 |

convertible on freeway, top down | 95 | 1.1 |

rock concert | 120 | 20 |

eardrum perforates | 160 | 2,000 |

shuttle launch | 180 | 20,000 |

### Example: Shure SM58

( The following info is taken from specs )

**Sensitivity = -54.5dBV/Pa (1.85mV) where 1 Pa = 94dBSPL**

Interpreting this, we see that a fairly loud sound ( 94dBSPL, from a pressure of 1 Pa) will result in -54.5dBV signal. Using our online calculator, we get that it is a voltage of .0018Volts = 1.8mVolts.

If we want to get this signal up to professional line level ( +4dBu ), we will need to amplify it. This is the job of a microphone pre-amp. How much gain do we need to the pre-amp to be capable of?

First off, the sensitivity is given in dBV. We need to be careful of units, and convert this to dBu. Again, using the online calculator we get that:

-54.5dBV = -52.3dBu *(to convert, add 2.2 to the dBV value)*

So the gain needed …

+4dBu - (-52.3dBu) = +4dBu + 52.3dBu = 56.3dB of gain.

So typical mic preamps have at least 60dB of gain, and perhaps more for additional headroom. ( The Universal Audio Solo/610 has a max of 61dB of gain.