This tool converts from dB (deciBel) to a linear value.

**Formula**

If the ratio represents power. For example the output power divided by the input power, then

**P _{linear} = P_{OUT}/P_{IN}**

and

**P _{dB} = 10*Log_{10}(P_{linear})**

or

**P _{linear}** =

**10**

^{(PdB/10)}If the ratio represents output voltage divided by the input voltage, then

**V _{linear} = V_{OUT}/V_{IN}**

since **P _{linear} = P_{OUT}/P_{IN}**

then, **P _{linear} =**

**(V**/

_{OUT}^{2}/R_{OUT})/(V_{IN}^{2}**R**

_{IN})if the input impedance is the same as the output impedance, then **R _{OUT}** =

**R**

_{IN}Also,

**P _{dB} = 10*Log_{10}( V_{OUT}/V_{IN})**

^{2}

or **P _{dB} = 20*Log_{10}(V_{linear})**

**V _{linear}** =

**10**

^{(PdB/20)}**Example **application

**How to use the linear to dB calculator**

- Enter the dB value
- Use the radio button to indicate if itβs a power or voltage ratio
- The tool will calculate the power or voltage ratio

**Example calculation**

Letβs say an amplifier module amplifies the input signal power by 30 dB.

In this case, the ratio of output to input power expressed as a linear number is 1000.

The ratio of output to input voltage expressed as a linear number is 31.62.

**Background**

The dB scale is a convenient way to represent both large and small numbers. For instance, 10000000000 = 100 dB while 0.0000000001 = -100 dB.

Numbers represented on a dB scale are typically ratios and percentages of **power** and **amplitude**. [1]

**A ratio has no units.** For instance, the ratio of two power levels 3 Watt to 2 Watt is 3/2 or 1.5. When performing the division, the units in the numerator and denominator cancel each other out and as a result the linear ratio has no units. *It’s important to ensure that the numerator and denominator have the same units. For instance, one cannot be Watt and the other milliWatt.*

When we ask the general question: How many times is one power level greater than another? The answer to this can be expressed in dB. As well, in reverse, dB can be converted to times.

For example, if a number A is 100 times greater than another number B, then on the log scale we can say that A is 10*Log_{10}(100) = 20 dB greater than B. The assumption is that A and B are power levels.

**Linear to dB Table**

This table presents linear equivalent over the range -100 dB to +100 dB.

dB | Linear Power |
---|---|

-100 | 1.0000E-10 |

-99 | 1.2589E-10 |

-98 | 1.5849E-10 |

-97 | 1.9953E-10 |

-96 | 2.5119E-10 |

-95 | 3.1623E-10 |

-94 | 3.9811E-10 |

-93 | 5.0119E-10 |

-92 | 6.3096E-10 |

-91 | 7.9433E-10 |

-90 | 1.0000E-09 |

-89 | 1.2589E-09 |

-88 | 1.5849E-09 |

-87 | 1.9953E-09 |

-86 | 2.5119E-09 |

-85 | 3.1623E-09 |

-84 | 3.9811E-09 |

-83 | 5.0119E-09 |

-82 | 6.3096E-09 |

-81 | 7.9433E-09 |

-80 | 1.0000E-08 |

-79 | 1.2589E-08 |

-78 | 1.5849E-08 |

-77 | 1.9953E-08 |

-76 | 2.5119E-08 |

-75 | 3.1623E-08 |

-74 | 3.9811E-08 |

-73 | 5.0119E-08 |

-72 | 6.3096E-08 |

-71 | 7.9433E-08 |

-70 | 1.0000E-07 |

-69 | 1.2589E-07 |

-68 | 1.5849E-07 |

-67 | 1.9953E-07 |

-66 | 2.5119E-07 |

-65 | 3.1623E-07 |

-64 | 3.9811E-07 |

-63 | 5.0119E-07 |

-62 | 6.3096E-07 |

-61 | 7.9433E-07 |

-60 | 1.0000E-06 |

-59 | 1.2589E-06 |

-58 | 1.5849E-06 |

-57 | 1.9953E-06 |

-56 | 2.5119E-06 |

-55 | 3.1623E-06 |

-54 | 3.9811E-06 |

-53 | 5.0119E-06 |

-52 | 6.3096E-06 |

-51 | 7.9433E-06 |

-50 | 1.0000E-05 |

-49 | 1.2589E-05 |

-48 | 1.5849E-05 |

-47 | 1.9953E-05 |

-46 | 2.5119E-05 |

-45 | 3.1623E-05 |

-44 | 3.9811E-05 |

-43 | 5.0119E-05 |

-42 | 6.3096E-05 |

-41 | 7.9433E-05 |

-40 | 1.0000E-04 |

-39 | 1.2589E-04 |

-38 | 1.5849E-04 |

-37 | 1.9953E-04 |

-36 | 2.5119E-04 |

-35 | 3.1623E-04 |

-34 | 3.9811E-04 |

-33 | 5.0119E-04 |

-32 | 6.3096E-04 |

-31 | 7.9433E-04 |

-30 | 1.0000E-03 |

-29 | 1.2589E-03 |

-28 | 1.5849E-03 |

-27 | 1.9953E-03 |

-26 | 2.5119E-03 |

-25 | 3.1623E-03 |

-24 | 3.9811E-03 |

-23 | 5.0119E-03 |

-22 | 6.3096E-03 |

-21 | 7.9433E-03 |

-20 | 1.0000E-02 |

-19 | 1.2589E-02 |

-18 | 1.5849E-02 |

-17 | 1.9953E-02 |

-16 | 2.5119E-02 |

-15 | 3.1623E-02 |

-14 | 3.9811E-02 |

-13 | 5.0119E-02 |

-12 | 6.3096E-02 |

-11 | 7.9433E-02 |

-10 | 1.0000E-01 |

-9 | 1.2589E-01 |

-8 | 1.5849E-01 |

-7 | 1.9953E-01 |

-6 | 2.5119E-01 |

-5 | 3.1623E-01 |

-4 | 3.9811E-01 |

-3 | 5.0119E-01 |

-2 | 6.3096E-01 |

-1 | 7.9433E-01 |

0 | 1.0000E+00 |

1 | 1.2589E+00 |

2 | 1.5849E+00 |

3 | 1.9953E+00 |

4 | 2.5119E+00 |

5 | 3.1623E+00 |

6 | 3.9811E+00 |

7 | 5.0119E+00 |

8 | 6.3096E+00 |

9 | 7.9433E+00 |

10 | 1.0000E+01 |

11 | 1.2589E+01 |

12 | 1.5849E+01 |

13 | 1.9953E+01 |

14 | 2.5119E+01 |

15 | 3.1623E+01 |

16 | 3.9811E+01 |

17 | 5.0119E+01 |

18 | 6.3096E+01 |

19 | 7.9433E+01 |

20 | 1.0000E+02 |

21 | 1.2589E+02 |

22 | 1.5849E+02 |

23 | 1.9953E+02 |

24 | 2.5119E+02 |

25 | 3.1623E+02 |

26 | 3.9811E+02 |

27 | 5.0119E+02 |

28 | 6.3096E+02 |

29 | 7.9433E+02 |

30 | 1.0000E+03 |

31 | 1.2589E+03 |

32 | 1.5849E+03 |

33 | 1.9953E+03 |

34 | 2.5119E+03 |

35 | 3.1623E+03 |

36 | 3.9811E+03 |

37 | 5.0119E+03 |

38 | 6.3096E+03 |

39 | 7.9433E+03 |

40 | 1.0000E+04 |

41 | 1.2589E+04 |

42 | 1.5849E+04 |

43 | 1.9953E+04 |

44 | 2.5119E+04 |

45 | 3.1623E+04 |

46 | 3.9811E+04 |

47 | 5.0119E+04 |

48 | 6.3096E+04 |

49 | 7.9433E+04 |

50 | 1.0000E+05 |

51 | 1.2589E+05 |

52 | 1.5849E+05 |

53 | 1.9953E+05 |

54 | 2.5119E+05 |

55 | 3.1623E+05 |

56 | 3.9811E+05 |

57 | 5.0119E+05 |

58 | 6.3096E+05 |

59 | 7.9433E+05 |

60 | 1.0000E+06 |

61 | 1.2589E+06 |

62 | 1.5849E+06 |

63 | 1.9953E+06 |

64 | 2.5119E+06 |

65 | 3.1623E+06 |

66 | 3.9811E+06 |

67 | 5.0119E+06 |

68 | 6.3096E+06 |

69 | 7.9433E+06 |

70 | 1.0000E+07 |

71 | 1.2589E+07 |

72 | 1.5849E+07 |

73 | 1.9953E+07 |

74 | 2.5119E+07 |

75 | 3.1623E+07 |

76 | 3.9811E+07 |

77 | 5.0119E+07 |

78 | 6.3096E+07 |

79 | 7.9433E+07 |

80 | 1.0000E+08 |

81 | 1.2589E+08 |

82 | 1.5849E+08 |

83 | 1.9953E+08 |

84 | 2.5119E+08 |

85 | 3.1623E+08 |

86 | 3.9811E+08 |

87 | 5.0119E+08 |

88 | 6.3096E+08 |

89 | 7.9433E+08 |

90 | 1.0000E+09 |

91 | 1.2589E+09 |

92 | 1.5849E+09 |

93 | 1.9953E+09 |

94 | 2.5119E+09 |

95 | 3.1623E+09 |

96 | 3.9811E+09 |

97 | 5.0119E+09 |

98 | 6.3096E+09 |

99 | 7.9433E+09 |

100 | 1.0000E+10 |

**References**

[1] deciBel on Wikipedia