by Charles Miller

Recently I found myself in a state somewhere between flummoxed and tongue-tied when trying to explain the inverse-square law to a client who only wanted to better understand why I had moved his Wi-Fi router from one side of the room to the other, and why that small change made such a big difference. In science, the inverse-square law states that the signal strength of a radio signal is inversely proportional to the square of the distance between the source (Wi-Fi Access Point) and the device (your laptop) connected to it… not that what you just read makes that any clearer. Next time I will just stick to saying "closer is better."

Anyone who has ever used Wi-Fi probably understands that the best connection is to be found close to the Wi-Fi Access Point (AP) and for the purposes of this discussion I will stipulate it is okay to call the AP a "modem" or "router" even though those names are not technically correct.

The reason the strength of a Wi-Fi signal falls off so precipitously as you move further away is explained by that aforementioned inverse square law. Logically, if you are using a Wi-Fi connected device that is five feet away and you move to a position ten feet away, then you might assume that moving twice as far away from the Wi-Fi Access Point would reduce the strength of the Wi-Fi signal by half. That is perfectly logical, but it is also dead wrong.

Applying the inverse square law proves that the power of the signal decreases with the square of the distance, leading to a more pronounced drop in signal strength as you move further away. When the distance between your tablet or smart phone and the Access Point is doubled, the signal is not reduced by half but is reduced to only one forth the original value. If you tripled the distance the signal strength is not reduced to one third but is reduced to only one-ninth of its original value. When the distance is quadrupled, the signal strength is reduced to a paltry one-sixteenth of the original value. The signal strength between two devices decreases more rapidly than a simple linear reduction, and this is why when you are talking on your cell phone you can sometimes take two steps in the wrong direction and completely lose your signal.

It is impossible to accurately translate any of this into precise linear measurements of feet. yards, or meters because circumstances differ. In one environment a Wi-Fi signal might degrade by 50% at 10 feet while in another setting it would degrade by 50% only beyond 50 feet or more. Factors such as materials used in walls or floors, furniture, and interference from other electronic devices all have to be figured in. This is something a trained professional is better equipped to recognize.

A situation I once encountered was a client who had a huge wire-metal birdcage next to her Access Point, and that birdcage soaked up all the Wi-Fi signal like a sponge. She could literally be standing ten feet away from her AP with the birdcage in between, and not get a reliable Wi-Fi connection. The wavelength of the Wi-Fi radio frequency is roughly 12.5 centimeters and a wire mesh of 1/10th of the wavelength will effectively block it. 12 millimeters is almost exactly how far apart the wires of the birdcage were.

Fortunately, all these calculations work the other way around when you are trying to find a better Wi-Fi connection. Reducing by half the distance between your device and the AP to which you connect it does not double the signal strength, it could quadruple the signal strength. And a stronger Wi-Fi signal almost always translates into a faster internet connection. Closer is better.

So maybe now it is clearer why I suggested to my client that his smart TV and his Wi-Fi access point should be moved closer together.

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Charles Miller is a freelance computer consultant with decades of IT experience and a Texan with a lifetime love for Mexico. The opinions expressed are his own. He may be contacted at 415-101-8528 or email FAQ8 (at) SMAguru.com.

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