Decibels have never really made a lot of sense to me, though I memorized the relevant numbers to pass both my Technician and General class ham radio operator license tests.

I mean, 3dB = 2:1, 6dB = 3:1 and 10dB = 10:1? What sense does that make? And its bothered me that I didn’t know how to figure out where those numbers came from.

But I’ve finally found a formula to do the conversion from dB to a power ratio that I can remember and makes a sort of sense, especially when dealing with partial decibel numbers like “2.8 dB”.

So here it is:

Research Gate

Ratio = 10^(dB/10)

So using 2.8dB from the 2016-2020 Amateur Extra question pool (E9A15), 2.8 dB converts to 1.905 power ratio for calculating effective radiated power.

**10^(2.8/10) = 1.905**

And that means that a station with 150 watts of transmitter power and 2dB of feed line loss and 2.2dB of duplexer loss plus 7dBd antenna gain has an effective radiated power of 286 watts.

**Total gain = 7 dBd – 2 dB – 2.2 dB = 2.8 dBd or a 1.905 power ratio.**

**150 watts x 1.905 = 286 watts effective radiated power.**

Simple! Now I can move on to the next question in my study guide. Just 55% more to go!

Addendum: See solving decimal exponents here to deal with the 10^0.28 part of the equation without a scientific calculator.