Decibel Formula for Power

The formula for calculating a decibel change for power is:

dB = 10 * log (P₁ / P_r)

Where:

dB = The change in decibels
P₁ = The new or measured power measurement
P_r = The original or reference power measurement

The result of this formula will be either positive or negative. If it is positive, the result is an increase, or gain. If it is negative, the result is a decrease, or loss.

10 log Decibel Calculation Example

An audio amplifier is delivering 15 watts, and its output is decreased to 5 watts. What is the change in decibels?

Step one:

Ask yourself, "What do I expect to happen?" If the amplifier will be delivering less power, then there will be less sound coming out of the system. In the AV industry, this is called a "loss."

Step two:

Which number do you put first? The number used as the Pr is where you start your measurement. In this example, the 15 would be the Pr.

Step three:

Calculate the log.

In this example, the problem concerns power. Therefore, you need to use the 10 log formula. In step two, you completed the division. Now enter 0.33 in your calculator and press the "log" button.

10 * log (P₁/ P₂)

10 * log (0.33)

10 * (-0.48)

Step four:

Multiply -0.48 by 10.

10 * (-0.48)

The answer is: - 4.8 dB

Decibel Formula for Distance

The formula for calculating decibel changes in sound pressure level over distance is:

dB = 20 * log (D₁ / D₂)

Where:

dB = The change in decibels
D₁ = The original or reference distance
D₂ = The new or measured distance

The result of this calculation will be either positive or negative. If it is positive, the result is an increase, or gain. If it is negative, the result is a decrease, or loss.

Decibel Formula for Voltage

The formula for calculating decibel changes in voltage is:

dB = 20 * log (V₁ / V_r)

Where:

dB = The change in decibels
V₁ = The new or measured voltage
V_r = The original or reference voltage

The result of this calculation will be either positive or negative. If it is positive, the result is an increase, or gain. If it is negative, the result is a decrease, or loss.

20 log Decibel Calculation Example

Assume a loudspeaker is generating 80 dBSPL at a distance of 22 feet (7 m) away from the source outdoors. What would the level be at 88 feet (27 m) away?

Step one:

Ask yourself, "What will happen?" If a listener moves from 22 feet (7 m) to 88 feet (27 m) away, the sound will be perceived as softer.

Step two:

Which number do you put first? If you expect a gain, place the higher number first. If you expect a loss, place the smaller number first. In this example, you are expecting a loss so the small number, 22, goes first. (22 / 88).

Step three:

Now that you have calculated the amount of loss, the impact of the change needs to be determined. Add the results from step two to the original dB SPL measurement.

80 + (-12) = 68 dB SPL

80 - 12 = 68 dBSPL

The sound pressure level at 88 feet (27 m) from the point source is 68 dB SPL.