Calculating Power Ratios from Decibels

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:

Ratio = 10^(dB/10)

Research Gate

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.