The dB or decibel

The dB is used to compare two values (numerator vs. denominator) in a logarithmic scale.  It may be used as a relative (both values are variable) or absolute (one value is set as a reference) metric.

 

Formula

For Power Quantities

(such as Watts or Watts/m2 )
dB = 10 log W
W0

For Non-Power Quantities

(such as Pa, V, inches/sec, G)
dB = 10 log A2
A20
or
dB = 20 log A
A0

dB Reference

Quantity

Formula

Reference

Voltage (dBV) Non Power 1 VRMS
dBm Power 1 mWatt
dBu Non Power 0.775 VRMS
Sound Pressure Non Power 20 μPa
Sound Intensity Power 1 pWatt/m2
Sound Power Power 1 pWatt
Acceleration Non Power 1 µm/s2 *
Velocity Non Power 1 nm/s *
*Non-standard references often used especially in USA and machine vibration

 

dB to Ratio Converstion

for negative dB, use reciprocal of ratio
dB Non
Power

Ratio
Power
Ratio

 

 

dB Non
Power

Ratio
Power
Ratio
0.0 1.000 1.000   6 1.995 3.981
0.1 1.012 1.023   7 2.239 5.012
0.2 1.023 1.047   8 2.512 6.310
0.3 1.035 1.072   9 2.818 7.943
0.4 1.047 1.096   10 3.162 10.000
0.5 1.059 1.122   12 3.981 15.849
0.6 1.072 1.148   14 5.012 25.119
0.7 1.084 1.175   16 6.310 39.811
0.8 1.096 1.202   18 7.943 63.096
0.9 1.109 1.230   20 10.000 1.0E+02
1.0 1.122 1.259   30 31.623 1.0E+03
1.5 1.189 1.413   40 100.000 1.0E+04
2.0 1.259 1.585   50 316.228 1.0E+05
3.0 1.413 1.995   60 1.0E+03 1.0E+06
4.0 1.585 2.512   70 3.2E+03 1.0E+07
5.0 1.778 3.162   80 1.0E+04 1.0E+08
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