String length in pixels in Java

Question 1

that does not use any GUI components?

It depends on what you mean here. I'm assuming you mean you want to do it without receiving a HeadlessException.

The best way is with a BufferedImage. AFAIK, this won't throw a HeadlessException:

Font font = ... ;
BufferedImage img = new BufferedImage(1, 1, BufferedImage.TYPE_INT_ARGB);
FontMetrics fm = img.getGraphics().getFontMetrics(font);
int width = fm.stringWidth("Your string");

Other than using something like this, I don't think you can. You need a graphics context in order to create a FontMetrics and give you font size information.

Question 2

You can use the Graphics2D object to get the font bounds (including the width):

Graphics2D g2d = ...
Font font = ...
Rectangle2D f = font.getStringBounds("hello world!", g2d.getFontRenderContext());

But that depends on how you will get the Graphics2D object (for example from an Image).

Question 3

This gives the output of (137.0, 15.09375) for me. I have no idea what the units are, but it certainly looks proportionally correct and doesn't use Graphics2D directly.

    Font f = new Font("Ariel", Font.PLAIN, 12);
    Rectangle2D r = f.getStringBounds("Hello World! Hello World!", new FontRenderContext(null, RenderingHints.VALUE_TEXT_ANTIALIAS_DEFAULT, RenderingHints.VALUE_FRACTIONALMETRICS_DEFAULT));
    System.out.println("(" + r.getWidth() + ", " + r.getHeight() + ")");

Question 4

I needed to get length and width of a string before paintComponent was called so I could size the enclosing panel to the text dimensions. None of these techniques provided a sufficiently width and I did not have a Graphics object available. I resolved the issue by setting my font to "Monospaced".