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The galaxy in the below image is a reconstruction of the Milky Way. It's about 100,000 light-years across. The teeny tiny green circle is 200 light-years.
That's how far our radio broadcasts have traveled to date.
What's more, our messages are often distorted by our ionosphere, making them little more than garbled noise to anyone beyond Earth. And unfortunately, the signals that aren't distorted are so weak by the time they're 100 light-years away that they're basically undetectable anyway.
As a result, if there are any intelligent aliens out there, they probably can't hear us — unless they are absurdly close to Earth.
Calculating the distance
Italian inventor and electrical engineer Guglielmo Marconi made the first radio broadcast in 1895. However, long-range radio transmission technologies didn’t arise until the early 1900s. That means we’ve been sending signals into space for about 100 years.
Light can travel 100 light-years in 100 years (obviously). However, since our radio signals are broadcast in all directions, we need to account for both ends of the expanding sphere. This effectively doubles the range.
So when it comes to the total distance, our radio broadcasts have traveled 200 light-years.
If you want to do things the hard way and calculate the miles or kilometers yourself, here’s how you do it.
The speed of light is about 300,000,000 meters a second. You need to multiply that by the number of seconds in a year (31,536,000) to get the total distance light travels in a year, which gives us a total of 9,460,800,000,000,000 meters a year.
This translates to 9.4 quadrillion meters, 9.4 trillion km, or 5.8 trillion miles.
Now, multiple that by the 100 years we have been broadcasting radio signals, and you get 940 trillion km (580 trillion miles).
Since these signals radiate in all directions, you need to double that distance, and you get the following: Our radio broadcasts cover an area about 1.8 quadrillion km across (1.1 quadrillion miles) — or 200 light-years.
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