Admittedly, the formulas to convert between decibel-milliwatts (dBm) and milliwatts (mW) look a little intimidating.

dBm = 10 × log₁₀(mW)

mW = 10^{(dBm ÷ 10)}

Performing logarithms and exponents aren’t things that most people do easily in their heads.

The goal here is to show you a couple very simple tools that you can use to conquer these calculations:

• The Rule of 10s and 3s
• Spreadsheet Formulas

The Rule of 10s and 3s

The rule of 10s and 3s is a very simple way to do some quick and basic math to get you a very close approximation of how dB gain or loss affects absolute power in mW. If you know how to add, subtract, multiply, and divide, you are very capable of using this trick.

One area where many seem to struggle appears to come from remembering which operation goes with which units. This distinction is absolutely critical to success here.

• When dealing with dB, you will add or subtract
• When dealing with mW, you will multiply or divide

Now, on to the technique. It has been stated in a few different ways to help the mental connection really sink in.

10dB Gain	mW multiplied by 10	mW × 10	10 Times
10dB Loss	mW divided by 10	mW ÷ 10	A Tenth
3dB Gain	mW multiplied by 2	mW × 2	Double
3dB Loss	mW divided by 2	mW ÷ 2	Halved

An old car stereo of mine displayed volume in terms of decibels. If I turned up by 3dB, it is was twice as loud as it was before.

As a more relevant example, consider a transmitter outputting a signal at 10mW that is connected to a cable with 3dB loss which is subsequently connected to a 10dB gain antenna.

• The power at the other end of this cable with 3dB loss is halved, so the power entering the antenna is 10mW ÷ 2 = 5mW
• The power being radiated by the antenna with 10dB gain means 10 times the power, 5mW × 10 = 50mW

What if I need to know about a gain or loss that isn’t 10 or 3 dB? As implied by the words “gain” and “loss”, we can simply add and subtract dB values together. From the example above, we had a 3dB loss from the cable and a 10dB gain from the antenna, or -3dB + 10dB = 7dB.

Whenever we have a dB value that is not a 10 or a 3, we want to expand that number out using the 10s and 3s that we do know how to work with. Straight from the above example, we see that 7dB is equivalent to a 10dB gain and a 3dB loss. We can express this in several ways and they’re all the same:

• 7dB = 10dB + (-3dB) = 10dB – 3dB = -3dB + 10dB

You will benefit greatly by working through a very simple exercise, to express the numbers 1 through 10 in terms of 10s and 3s. For best results, give it a try before looking at the solutions below. There may be multiple ways to get to the same answer and remember that with addition and subtraction, order doesn’t matter.

1	= 10 – 3 – 3 – 3
2	= 3 + 3 + 3 + 3 – 10
3	= 3
4	= 10 – 3 – 3
5	= 3 + 3 + 3 + 3 + 3 – 10
6	= 3 + 3
7	= 10 – 3
8	= 10 + 10 – 3 – 3 – 3 – 3
9	= 3 + 3 + 3
10	= 10

As a final point, mentioned earlier was that this rule gives us a very close approximation. To break this down further, working with 10s will give us exact numbers while working with 3s will give us close but approximate numbers. We can see this when we look at the actual numbers here:

dBm	mW
0	1.000
3	1.995
10	10.000

Notice that 0dBm is equivalent to 1mW, 3dBm is just about 2 times, or double, 1mW, and 10dBm is exactly 10 times 1mW.

Spreadsheet Formulas

Now let’s be real. Unless we’re doing a very simple calculation using multiples of 10s and/or 3s, or we happen to be studying for an exam, we are likely going to use tools available to us to get the best results, i.e. a calculator.

You’re welcome to memorize the formulas or refer back to this page whenever you need them, but I am personally a big fan of spreadsheets. You can easily create your own spreadsheet using something like Microsoft Excel or Google Sheets to perform the required calculations using the following formula syntax. In fact, this is exactly what I did to generate the numbers in the table above!

To calculate mW from dB, use 10^(x/10) where x is the dB value or the cell that contains the dB value.

To calculate dB from mW, use 10*LOG10(x) where x is the mW value or the cell that contains the mW value.