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I've had occasion to typeset extraordinarily large matrices, which I didn't seriously expect anyone to expect in detail (without a computer) or print, but I needed it to be obvious that they were completely explicit and written down somewhere.

By trial and error, I found a really large paper size that would compile (about 5.5m) in pdflatex and fit my matrices on a reasonable number of sheets. (I used the geometry package to choose custom page sizes.) But it would have been easier if I'd been able to find out:

What are the limitations on paper sizes in pdflatex?

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From the immensely useful TeX by Topic:

\maxdimen 16383.99999pt; the largest legal dimension.

and

Internally TEX works with multiples of a smallest dimension: the scaled point. Dimensions larger (in absolute value) than 2^30 − 1sp, which is about 5.75 metres or 18.9 feet, are illegal.

Knuth delivered a beautiful extended dig at "modern" software development practices at the 2010 TUG meeting, during the early part of which he referred to the value of \maxdimen. I can't work out if he was serious when he suggested it had been a mistake to fix the largest dimension in TeX at this rather small value.

Perhaps it is worth mentioning that as far as I know, pdflatex does not apply any more restrictive limits than TeX itself for this application. So the limitation that is relevant here is the internal TeX one.

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    I'll keep that in mind if I ever want to typeset a billboard using TeX.
    – PersonX
    Commented Jul 28, 2010 at 15:19
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    Of course, typesetting a billboard could be done by upscaling a smaller document. It's not like one needs 72.27sp per inch resolution...
    – András Salamon
    Commented Jul 28, 2010 at 16:51
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    Personally, I'm always peeved that TeX can't deal with dimensions on the order of 1 farshimmelt potrzebie.
    – Sharpie
    Commented May 10, 2011 at 2:32
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Since you mention pdfTeX, I assume that you want to produce PDFs. The PDF norm mentions this "architectural limit":

The minimum page size should be 3 by 3 units in default user space; the maximum should be 14,400 by 14,400 units. In versions of PDF earlier than 1.6, the size of the default user space unit was fixed at 1⁄72 inch, yielding a minimum of approximately 0.04 by 0.04 inch and a maximum of 200 by 200 inches. Beginning with PDF 1.6, the size of the unit may be set on a page-by-page basis; the default remains at 1/ 72 inch.

200 inches are 508 cm. While this limit is probably not enforced by any PDF-producing program in the TeX world, I'd advise against exceeding it.

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    These 14,400 units are in user space. But the default user space unit of 1/72 inch (the minimum) can be changed to a maximum of 75,000 (that is since PDF-1.6, I believe). That gives you a maximum of 381 kilometers in (virtual) page dimensions!
    – Kurt Pfeifle
    Commented May 8, 2015 at 4:03

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