Decibel
Power quantities

When referring to measurements of power quantities, a ratio can be expressed as a level in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P (reference power) is represented by L, that ratio expressed in decibels, which is calculated using the formula:

The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel). P and P must measure the same type of quantity, and have the same units before calculating the ratio. If P = P in the above equation, then L = 0. If P is greater than P then L is positive; if P is less than P then L is negative.

Rearranging the above equation gives the following formula for P in terms of P and L:
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