If you just want to use AWT, then use Graphics.getFontMetrics (optionally specifying the font, for a non-default one) to get a FontMetrics and then FontMetrics.stringWidth to find the width for the specified string.
For example, if you have a Graphics variable called g, you’d use:
int width = g.getFontMetrics().stringWidth(text);
For other toolkits, you’ll need to give us more information – it’s always going to be toolkit-dependent.