Estimating Collisions in URL Shortening

In this blog post I estimate the time before the first collision for URL shorteners such as bit.ly occurs.

bit.ly is an example of a URL shortener. Other examples are: tinyurl.com and 7les.com. Although the details differ the general idea is similar. A shortener takes a long url for example

http://www.thelongestlistofthelongeststuffatthelongestdomainnameatlonglast.com/wearejustdoingthistobestupidnowsincethiscangoonforeverandeverandeverbutitstilllookskindaneatinthebrowsereventhoughitsabigwasteoftimeandenergyandhasnorealpointbutwehadtodoitanyways.html

and produces a short url, in this case http://bit.ly/2EnEgk. Because of the "limited" amount of short urls available, sooner or later there should be a collision i.e. two different long urls which produce the same short url.

Now lets take the bit.ly service as an example. It seems to produce short urls with a unique part of 6 characters, where the characters come from the alphabet of lower and upper Latin characters plus the digits. In total the alphabet contains 62 (= 26 + 26 + 10) characters. There are 6 position, each position allowing one of 62 characters for a total of 56800235580 (fifty-six billion, eight hundred million, two hundred thirty-five thousand, five hundred eighty) short urls.

I could not find any numbers telling how many urls are shortened by bit.ly per day. I am guestimating a figure of 1.000.000. This would give bit.ly approximately 56800 days, a little over 115 years, before they must return a colliding short url.

To summarize, within 115 years bit.ly will have produced a collision in their url shortening business. My advice for them. Register a new domain name and start over.