This tool calculates the times equivalent of a number in deciBels (dB).
Enter the dB difference between two numbers into the tool below and it will calculate the number of times one is larger than the other.
Formula
N = 10(dB/10)
or
dB = 10*Log10(N)
Example Calculations
If on the dB scale, a number X is 20 dB larger than another number Y, then X is 100 times Y.
Similarly if X is 10 dB smaller than Y, then use -10 dB in the calculator to find that X is 0.10 times Y. Also, in this case Y is 10 dB larger than X and therefore Y is 10 times X.
Background
In general deciBels (dB) is used to represent a ratio of amplitude or power. By extension, the equivalent linear quantity represents how many times an amplitude or power level is greater than another.
The conversion of dB to ratio is a common calculation used in various fields, such as telecommunications and audio engineering. dB is used to measure the intensity of a sound or signal relative to a reference level. On the other hand, ratio is a mathematical expression that shows the relationship between two quantities.
In the formula above we have used a 10*Log() relationship which is representative of Power. If we were comparing Voltage instead it would be 20*Log().
Application Example
Amplifier gain is the ratio of the output signal power to the input signal power. It is a fundamental parameter in the design and implementation of electronic circuits. Voltage gain is the most common type of gain used, but current or power gain may also be utilized.
If an amplifier’s power gain is 30 dB, this means that the output power will be 1000 times the input power. At 0 dB there is no amplification and the output power is equal to the input. In other words, it’s identical to or 1 times the input.
At negative values of dB, the amplifier is no longer amplifying. Instead it is attenuating the signal. Practically this can happen when the input signal is outside the operating range of the amplifier. At -10 dB, the output is 0.10 times the input.
dB to Times Table
The table below shows deciBel values converted to linear times. The dB scale is a convenient method to represent large numbers. For instance, 110000000000 is equivalent to 100 dB.
| dB | Times |
|---|---|
| -100 | 0.0000000001 |
| -90 | 0.000000001 |
| -80 | 0.00000001 |
| -70 | 0.0000001 |
| -60 | 0.000001 |
| -50 | 0.00001 |
| -40 | 0.0001 |
| -30 | 0.001 |
| -20 | 0.01 |
| -10 | 0.1 |
| 0 | 1 |
| 10 | 10 |
| 20 | 100 |
| 30 | 1000 |
| 40 | 10000 |
| 50 | 100000 |
| 60 | 1000000 |
| 70 | 10000000 |
| 80 | 100000000 |
| 90 | 1000000000 |
| 100 | 10000000000 |