How to calculate the number of rows (and columns in each row) a text takes in a JTextArea?

What am I doing wrong, what am I forgetting about?

Nothing, really. I modified your example to use “<=” on the width and to highlight a few features:

1. FontMetrics notes, “the advance of a String is not necessarily the sum of the advances of its characters measured in isolation…”

2. The preferred size of the text component matches the metric bounds pretty well for the widest line. This varies by font due to proportional spacing.

3. TextLayout shows even tighter bounds, but note the “baseline-relative coordinates.”

4. The getLineCount() method counts line.separator delimited lines, not wrapped lines.

line: Twas brillig and the slithy toves
line: Did gyre and gimble in the wabe;
line count: 2
preferred: java.awt.Dimension[width=207,height=48]
bounds1: java.awt.geom.Rectangle2D$Float[x=0.0,y=-12.568359,w=205.0,h=15.310547]
layout1: java.awt.geom.Rectangle2D$Float[x=0.0,y=-10.0,w=200.0,h=13.0]
bounds2: java.awt.geom.Rectangle2D$Float[x=0.0,y=-12.568359,w=207.0,h=15.310547]
layout2: java.awt.geom.Rectangle2D$Float[x=1.0,y=-10.0,w=205.0,h=13.0]

import java.awt.Dimension;
import java.awt.FontMetrics;
import java.awt.font.FontRenderContext;
import java.awt.font.TextLayout;
import java.util.ArrayList;
import java.util.List;
import javax.swing.JFrame;
import javax.swing.JTextArea;
import javax.swing.SwingUtilities;

/** #see http://stackoverflow.com/questions/5979795 */
public class TextAreaLine {

    private static final String text1 =
        "Twas brillig and the slithy toves\n";
    private static final String text2 =
        "Did gyre and gimble in the wabe;";
    private static final JTextArea ta = new JTextArea(text1 + text2);

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {

            @Override
            public void run() {
                display();
            }
        });
    }

    static void display() {
        JFrame f = new JFrame();
        ta.setWrapStyleWord(false);
        ta.setLineWrap(false);
        ta.setRows(3);
        f.add(ta);
        f.pack();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.setLocationRelativeTo(null);
        f.setVisible(true);
        FontMetrics fm = ta.getFontMetrics(ta.getFont());
        List<String> texts = new ArrayList<String>();
        Dimension d = ta.getPreferredSize();
        String text = ta.getText();
        String line = "";
        for (int i = 0; i < text.length(); i++) {
            char c = text.charAt(i);
            if (c != '\n') {
                if (fm.stringWidth(line + c) <= d.width) {
                    line += c;
                } else {
                    texts.add(line);
                    line = "" + c;
                }
            }
        }
        texts.add(line);
        for (String s : texts) {
            System.out.println("line: " + s);
        }
        System.out.println("line count: " + ta.getLineCount());
        System.out.println("preferred: " + d);
        System.out.println("bounds1: " + fm.getStringBounds(text1, null));
        FontRenderContext frc = new FontRenderContext(null, false, false);
        TextLayout layout = new TextLayout(text1, ta.getFont(), frc);
        System.out.println("layout1: " + layout.getBounds());
        System.out.println("bounds2: " + fm.getStringBounds(text2, null));
        layout = new TextLayout(text2, ta.getFont(), frc);
        System.out.println("layout2: " + layout.getBounds());
    }
}