What is the rule of squares?

The rule of squares, also known as the inverse-square law, is important to understand with any sort of broadcasting. It applies to TV antennas, satellites, and cell towers. Not only that, it even applies to cellular signal boosters. It will help you understand what’s happening anytime you’re dealing with signal over the air.

In mathematical terms…

The inverse-square law looks like this to mathematicians:

In more literary terms, it looks like this:

Any physical intensity will diminish in a manner inversely proportional to the square of the distance from the source of the intensity.

But if you are bamboozled by that, there’s a simpler way to explain it.

In layman’s terms…

The further away from the source of a signal, the weaker it is. When you double the distance between you and the source, the signal is only 1/4 as strong.

To look at that in a really vague way, signal strength goes down really fast as you walk away from the source of the signal.

What this means to you

The rule of squares explains why broadcast towers have to pump so much electricity through them, and why the signals are so weak when they get to you. It explains why satellite signals are so weak, and why cell boosters work best when you’re pretty close to the indoor antenna.

Here are a couple of real-world examples:

TV Towers

A typical television broadcast facility pumps 50,000 watts of electricity through the tower. At six feet away from the actual broadcast site, let’s say the effective power is already down to about 10,000 watts. Then, at 12 feet away it’s down to 2500 watts and at 24 feet away it’s down to 625 watts. At 48 feet away it’s down to 156 watts. Now, keep in mind, you need this signal to be received from 60 miles away and it’s getting weaker fast.

It’s a good thing that you can receive good signals with only about 1/10,000th of a watt because you can see how those numbers drop pretty quickly.

Cellular signal boosters

The same is true with a cellular signal booster. A typical home cell booster is amplifying a signal by about 100,000 times and rebroadcasting it. Within just four feet it’s down to only 10,000 times as strong. Within eight feet it’s 2,500 times as strong, and within 16 feet it’s down to 625 times as strong. That may still seem like an improvement but as you keep walking away, it keeps getting weaker to the point where within about 50 feet of open space there’s barely any benefit.

The neat thing about the rule of squares

I know this will blow your mind but this rule doesn’t care if you’re english or metric, if you use watts or dBm, none of it matters. It’s all relative. If you double the number of feet, you get 1/4 the number of watts. If you double the number of centimeters, you get one quarter the number of dBm. No matter what measurement you choose, even one you’ve made up like smoots, the effect is going to be the same. And really, it doesn’t matter what the difference is, what the actual numbers are, because it really boils down to this very common-sense statement:

If you’re going to amplify any sort of signal you’re going to need a lot of power because you’ll lose almost all of it really quickly.

And that, friends, is what really matters.

About the Author

Stuart Sweet
Stuart Sweet is the editor-in-chief of The Solid Signal Blog and a "master plumber" at Signal Group, LLC. He is the author of over 8,000 articles and longform tutorials including many posted here. Reach him by clicking on "Contact the Editor" at the bottom of this page.