Would love to hear your thoughts.
To contrast, a non-startup company has a viable business model, and simply "does what it does," not constantly attempting to reinvent itself as something else.
It sounds to me like it's a matter of attitude, rather than size, or business model, or age of the company.
Normal businesses that you would not consider a startup usually have only a few people or one person starting them. They usually take some money, from friends/family or an investor or bank. They work hard, long hours. Hell they probably could be in the tech sector. The key difference though is intent.
Normal businesses are looking to build a stable business with a viable income. Usually something akin to a mom and pop store or a restaurant. They tend to be risk averse, and have a business model in mind. Rarely does a normal business start without some sort of revenue source in place.
Startups on the other hand, while sharing a lot of traits with normal businesses, throw risk to the wind and a lot of the times have no revenue model in place (though that does not mean having one makes you a non-startup). Most startups are starting small, and trying to grow big. A lot of the time they are product based, but really startups can be service based just as easily. The main qualifier of a startup is lack of risk aversion and short to long term goals.
There are some edge cases here and there, startups that seem like normal businesses. A company that has a business model, is starting small, and not trying to immediately grow to huge. Some would consider this a normal business, but if the owner feels like it is a startup, then well it is.
Now I have no idea what that formula is, but I'm guessing its some calculation that we all do in our head based on our own ideas and in the end we say 'yup.. it's a startup..' or not.
At some point Google, Facebook, LinkedIn, Groupon etc.. all surpassed that level of 'Startup' and moved into the 'Big Company' field.
Can any math geeks out there put together something that reflects that ?
Likewise it doesn't necessarily need millions in revenue to be successful. Many exits have come from zero revenue.
The question is about what constitutes a startup, not what constitutes success.
I'd say that startup = a relatively new business. Hence the (slightly antiquated) term, "startup business."
A site that doesn't make money (or that doesn't have a business model) isn't a startup business, it's a website (or blog, or forum, or web app, etc.).