How to create HTML output that is "cooked" for browsers?

I hope this simple question has a simple answer...

I'm using ckeditor within a <textarea> and think it's great.  I can display WYSIWYG content, save it to a file, and re-display it perfectly.

What I'd like to do is to convert the content from ckeditor to "cooked" HTML form so that it can be echoed to a browser window as "normal" HTML. 

"Raw" Example: Uses the 'ampersand'-encoded forms, as in the replacebyclass.html example.

"Cooked" Example:Uses normal HTML markup tags, for headers, paragraph, etc.

If I could convert from raw to cooked HTML, then a non-ckeditor browser could display it in its WYSIWYG form.

Is there a way to output cooked HTML while posting from a ckeditor textarea?

Thanks!