There is no definitive size where it becomes necessary or ideal to use an external stylesheet. Size is one factor but there are others which come into play. For example, an external stylesheet can be cached by the browser. So if your visitors will be making multiple page requests that use the same stylesheet, the browser can cache that stylesheet which will give the user faster page loads and a better experience. It also saves your server load and bandwidth.
Conversely, if this is a one page website then having the browser have to make multiple requests for assets can slow down the page load and harm the user experience (although it would be minimal).
So this decision depends on what you're doing and how you're doing it.