After almost a work day’s worth of searching, I was able to find a solution to my dilemna. While JTextArea has a getLineCount() method to return the number of lines, I wanted a way to also detect wrapped lines since I wanted to set my component a fixed height if the maximum height limit is reached.
This method by user Jörg in the Java forum did the trick.
This custom made method of by Parth Gallen counts the number of words found in a String object. This method detects new lines to count them as another word whenever it encounters one. To use the method, simply call it like in the code below:
Here is the code for counting the words found in a String.