How Many Unique bit.ly Combinations Are There?
I was thinking randomly about how many bit.ly combinations there are and how much unique shortened URLs they can generate given their current construct. Here’s their construct:
- Up to 6 characters after bit.ly/
- Any mix of capitalized letters, lowercase letters, and numbers
If you limit the combinations to only ones where bit.ly is the domain (and not partner domains), and you presume they can go up to 6 characters (i.e. 1–6) as opposed to exactly 6 characters – how many total combinations are there? Any math whiz out there who can figure it out pretty quickly and enlighten us in the comments section? My small math brain was getting cramps thinking about it.
Given that they shorten 40–50 million URLS per day, I also wonder how long they can last on this construct. Probably a long time I suspect even including their growth. Random thought for the day, and thanks for the help.
Thinking About Thinking 
57,731,386,986?
Charlie – how’d you get to that answer? Sounds plausible.
Assumptions were…
* 62 possible characters (26 letters, each can be upper or lower case, plus 10 numerical characters).
* String can be 1-6 characters long
So, calculation would be (62^6)+(62^5)+(62^4)+(62^3)+(62^2)+(62^1)
Make sense?
I think the answer is actually slightly different. This is a permutations problem requiring the formula n!/(n-k)! where “n” is the set of values you are choosing from (in this case the number of possible characters) and “k” is the length of the string. Using 62 possible characters and strings of 6, 5, 4, 3, 2, 1 your formula would be:
62!/(56!) + 62!/(57!) + 62!/(58!) + 62!/(59!) + 62!/(60!) + 62!/(51!) =
45,051,792,964 possible permutations
actually nevermind, this would assume the use of each value only once, which in a bit.ly url isnt a requirement – so charlie’s answer is right. in any case, now you know how to solve for permutations!
Thanks for asking! I have always wondered the same thing, and keep waiting for the day they extend to 7 characters.
FYI: All bit.ly links use the same shortened URL regardless of “partner domains”
The shortened link for this post is:
http://bit.ly/c2Sp5a
http://j.mp/c2Sp5a
http://bitly.com/c2Sp5a
A post from TechCrunch this am is:
http://tcrn.ch/aa4WRS
http://bit.ly/aa4WRS
http://j.mp/aa4WRS
http://bitly.com/aa4WRS
However, you can’t hijack someone else’s shortened URL and try to make it your own:
http://tcrn.ch/c2Sp5a
Another consideration is custom domains longer than 6 characters like:
http://j.mp/HowManyUniquebitlyCombinationsAreThere
Other info:
if you add a plus sign ‘+’ to the end of any bit.ly link it will give you the stats on that link:
http://bit.ly/c2Sp5a+
even
http://bit.ly/HowManyUniquebitlyCombinationsAreThere+
and
http://tcrn.ch/aa4WRS+
I do believe Charlie has the right answer. The breakout is as follows:
62^6= 56800235584
62^5= 916132832
62^4= 14776336
62^3= 238328
62^2= 3844
62^1= 62
Total = 57,731,386,986
Just to clarify Larry, 62^6 represents the number of combos if you could ONLY have 6 characters. So you take the total combos for each number of characters possible and that should be the right number.
Thanks all – sounds like we have a consensus!
Thanks for figuring this out guys. I wasn’t able to sleep nights recently, worrying if I was using up more than my fair share of bit.lys. Now I can rest assured. Des
LoL 😀
duh?
The math behind that are so trivial that I don’t understand the point of this article. Was that a way to get some comments on your blog ?
Idea for a next blog post : now that we know how many different urls bit.ly can generate and the fact they are shortening 50million links a day, how long will they be able to shorten urls ? Seems complicated…
Sorry for being sarcastic, but seriously, it s VERY basic math…
Julien and Marco – I guess I’m just a mere math mortal. I can live with that!
I am brazilian, brazilian education is made for monkeys, and even I knew the answer for this math question 🙂
(I am brazilian, I can make jokes with brazilian educational system 🙂
Extra credit assignment:
If in the new land of IPv6, there exists a need to create unique IPs for each bit.ly URL.
So, if the entire scope of about 62^6 bit.ly URLs were mapped to IPv6 addresses, what is the minimum IPv6 subnet that could contain it?
Interesting thought. I had another one, I once typed in http://bit.ly into bit.ly and it gave me this: http://bit.ly/QtQET
is THAT shortening? LoL 😀
26 letters, upper and lower case, plus 0-9 = 72 unique characters, right?
72^6 = 139,314,069,504
@andrew
26 + 26 + 10 = 62
I wondered that bit ly’s don’t give URL’s that vary from 1 to 6 strings; they are always exactly 6 strings
So, the number should be
62 ^ 6 = 56, 800, 235, 584
Correct me if im wrong, but I never saw a bit ly less than 6 characters.
Which surely means bit.ly will run out in about 3 years. (50 thousand million @ 50 million per day = 1000 days = 3 years all approximations).So time to add an extra character?
If they upped it to 8 characters then it would be 62^8 = 2.18340106 × 10^14
Considering IPv4 allows 32 bits for an Internet Protocol address, and can therefore support 2^32 (4,294,967,296) addresses, IPv6 uses 128-bit addresses, so the new address space supports 2^128 (approximately 340 undecillion or 3.4×10^38) addresses.
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That’s a lot of possible shortened links! must be highly optimized to handle that. They’re also adding other small domains arn’t they?
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