I've got a textarea with a fixed height. When the user types text into the textarea a scrollbar will show up after the user typed some text in it.

How can I get the scrollbar height using jQuery or plain JavaScript? I've been searching for this for hours, but couldn't find anything. I can't just insert a div and get the scrollbar height via the div offset because a textarea is not allowed to have child elements.

Please don't give me a link to a jQuery Plug-In that does the job. I want to learn something.