Where the mark goes, and why the maths is the fiddly part
A watermark is one line of text drawn on the page, so the only real decision is where its starting point sits. For a horizontal mark in the center, that is half the page width to the left of the middle and a little below the middle. For a diagonal mark the text is rotated about its own start point, so the start point has to be placed before the visual center rather than on it - otherwise a 45-degree watermark drifts off toward a corner.
The mark is sized in points and measured with the font that will actually draw it, so a long word is centred on the page rather than hanging off one side. If the text turns out wider than the page - a long company name at a large size - the result says so instead of pretending the mark fits, and you can shorten the words or lower the size.
Top and bottom placements sit a fixed distance from the edge, which makes them behave like a header or a footer. The center placement is the one to use for the classic diagonal stamp, because it cannot collide with a page number or a running head.
A watermark is a label, not protection
Be clear about what this does and does not do. A text watermark is page content: anyone with a PDF editor can select the words and delete them, and the mark cannot stop copying, screenshots, re-typing or printing. It tells an honest reader that the document is a draft, a sample or confidential, and it makes a leaked copy recognisably yours - it does not enforce anything.
If the document genuinely must not be reused, the controls that can be enforced are different ones: encryption with a password, permission flags for printing and copying, or simply not sending the file. Those belong in tools built for it, and some of them need a server to hold the key. This page is honest about being the deterrent, not the lock.
The mark is drawn after the page content, so it always sits on top and cannot be hidden behind an image. That also means a heavy mark can cover words underneath, which is why the default is 25% opacity: visible on screen and in print, still readable underneath.
Fonts, size and what the file ends up containing
The text uses Helvetica, one of the fourteen fonts every PDF reader is expected to have. Nothing is embedded, so the file grows by a few hundred bytes per page rather than by a font file, and the output stays close to the size of the input. The trade-off is coverage: that font handles Latin letters, digits and everyday punctuation, not other writing systems, so the message has to be in plain English text.
Opacity is written as a transparency setting rather than by fading the colour, so the mark blends with whatever is underneath - white paper, a table, a photograph - instead of turning grey. The colour choices match the conventions people already read: red for confidential or unpaid, grey for a quiet draft, black when it has to be impossible to miss.
Nothing in your pages is rewritten. The original text, images and page geometry are untouched, which means the watermarked file is as searchable and as sharp as the file you put in; the only difference is one extra mark per page.