If two power levels, P1 and P2, are to be compared with deciBels, the relationship is defined as

(1) dB = 10 × log(P1/P2) where log is to Base-10

Here is an example: how much stronger in deciBels is a power of 25-Watts compared to 7-Watts?

- Given:

P1 = 25-Watts

P2 = 7-Watts

dB = 10 × log(P1/P2)

dB = 10 × log(25/7)

dB = 10 × log(3.57)

dB = 10 × 0.553

dB = 5.53

If we reverse the power ratio comparison, and ask how much weaker in deciBels is a power of 7-Watts compared to 25-Watts, the same formula is used:

- Given:

P1 = 7-Watts

P2 = 25-Watts

dB = 10 × log(P1/P2)

dB = 10 × log(7/25)

dB = 10 × log(0.28)

dB = 10 × -0.553

dB = -5.53

If a power ratio is stated in deciBels and we want to find the numerical ratio, we can manipulate equation 1 to solve for P1/P2. This gives:

(2) (P1/P2) = 10(dB/10)

For example, if a power ratio is expressed in deciBels to be 5.53 dB, what is the numerical ratio (P1/P2):

- Given:

dB = 5.53

(P1/P2) = 10(dB/10)

(P1/P2) = 10(5.53/10)

(P1/P2) = 10(0.533)

(P1/P2) = 3.57