Example Depot

// From within the paint() method
public void paint(Graphics g) {
    Graphics2D g2d = (Graphics2D)g;
    Font font = new Font("Serif", Font.PLAIN, 12);
    FontMetrics fontMetrics = g2d.getFontMetrics();

    int width = fontMetrics.stringWidth("aString");
    int height = fontMetrics.getHeight();
}

// From within a component
class MyComponent extends JComponent {
    MyComponent() {
        Font font = new Font("Serif", Font.PLAIN, 12);
        FontMetrics fontMetrics = getFontMetrics(font);

        int width = fontMetrics.stringWidth("aString");
        int height = fontMetrics.getHeight();
    }
}