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• Andrew Campbell

# Decibel Math

As a primer reading our section on What's a decibel? is recommended. How can you convert dBm to mW, and vice versa, easily?

When working in decibels, the rule of 3's and 10's can help make the math easier.

Rule of 3's:

For every 3 dB increase, the signal strength is doubled.

For every 3 dB decrease, the signal strength is halved.

Rule of 10's:

For every 10 dB increase, the signal strength is multipled by 10.

For every 10 dB decrease, the signal strength is divided by 10.

Memorize the table below for quick reference when doing decibel math. Let's run through some examples together...

What is 13 dBm in mW?

• First, we see how many 10s and 3s it takes to make up 13 dBm.

• We get 10 + 3 = 13.

• Next, we know that 10 dBm + 3 dBm = 13 dBm.

• Converting that to mW, we know 0 dBm = 1 mW.

• So, 1 mW x 10 x 2 = 20 mW. What is 36 dBm in mW?

• First, we see how many 10s and 3s it takes to make up 36 dBm.

• We get 10 + 10 + 10 + 3 + 3 = 36.

• Next, we know that 10 dBm + 10 dBm + 10 dBm + 3 dBm + 3 dBm = 36 dBm.

• Converting that to mW, we know 0 dBm = 1 mW.

• So, 1 mW x 10 x 10 x 10 x 2 x 2 = 4000 mW or 4 W. Are there any other shortcuts?

You can use subtraction/division to your advantage as well. For instance, you can go beyond the number you are trying to convert and subtract/divide to get your final answer. Let's look at an example...

What is 27 dBm in mW?

We are trying to see how many 10s and 3s add up to 27 dBm. We can do nine 3s, or we can do three 10s and subract one 3 (3x10 = 30-3 = 27).

Converting to mW, we know 0 dBm = 1 mW. 1x10x10x10/2 = 500 mW or 0.5 W. Using nine 3s, we would have gotten... 1x2x2x2x2x2x2x2x2x2 = 512 mW or 0.512 W. The rules of 3s and 10s are already an approximation of the decibel math, so the difference between 512 mW and 500 mW is negligible and the calculation is suitable for most Wi-Fi calculations.

What about every other number?

We know how to solve for the powers of 3s and 10s, we know 0 dBm = 1 mW, we solved for 13, 27, and 36 dBm. But, what about the numbers in between?

It is easiest to write out all the numbers between 0 dBm and 36 dBm, which is the maximum allowable EIRP by the FCC. After writting out what we know, we can use the rule of 3s to work our way backwards.

We know that 10 dBm is 10 mW (1x10). Knowing that we can subtract 3 to get to 7 dBm (5 mW), then another 3 to get to 4 dBm (2.5 mW), and another 3 to get to 1 dBm (1.25 mW).

Next, we know that 20 dBm is 100 mW (1x10x10). Knowing that we can subtract 3 to get to 17 dBm (50 mW), then another 3 to get to 14 dBm (25 mW). Continue this process all the way down to 2 dBm (1.56 mW).

Values highlighted in orange are commonly used in the Wi-Fi industry. See All