For perfect binding (a glued, square spine), the spine width follows directly from how thick the paper block is:
spine (mm) = (page count ÷ 2) × caliper (mm per sheet)
The division by two is the part people get wrong. Page count is pages, and caliper is quoted per sheet. One sheet has two pages — front and back — so 200 pages is 100 sheets.
A 200-page book on a paper with a 0.1 mm caliper:
If you get the spine wrong by 2 mm, the cover either wraps short of the text block or overhangs it. Both look like a manufacturing fault, and both are expensive to fix after printing.
Do not guess caliper from gsm. GSM is weight per area; caliper is thickness, and two papers of the same gsm can differ noticeably in bulk. An uncoated 80 gsm book paper and a coated 90 gsm art paper can have similar thickness, while two different uncoated 80 gsm stocks may not.
The caliper depends on the specific stock, the finish and the batch. Ask your paper merchant or printer for the caliper figure, or measure a known quantity of sheets with a micrometer: 100 sheets measured at 10 mm means 0.1 mm per sheet.
One more variable: caliper is measured at a specified pressure and varies with humidity. Paper swells in damp air. A spine calculated to two decimal places in a dry room can be visibly off in a humid one, which is why printers build in tolerance rather than trusting an exact figure.
A saddle-stitched booklet (stapled through the fold) has no spine to calculate — but it has creep, also called shingling or push-out. The inner pages sit further from the fold than the outer ones, so if the booklet is trimmed flush after folding, the inner pages lose more of their outer margin than the outer pages do.
Creep grows roughly linearly towards the centre. On a thin 16-page booklet it is a fraction of a millimetre and can be ignored. On a 64-page booklet on heavy stock, the innermost pages can push out by several millimetres and the outer margin visibly shrinks unless the layout compensates.
The usual fixes are to reduce the outer margin on inner pages before printing, or simply to keep margins generous enough that creep never reaches the text.
For a perfect-bound paperback, no — the spine is the text block, and the cover wraps around the outside of it. For a hardcover, the spine is formed by the case boards and the text block is inset, which is a different calculation and usually handled by the binder rather than by you.
Books are printed in sections, and a section is a multiple of four pages. An odd page count has to be padded with blank pages until it reaches the printer’s section size, so the spine should be calculated on the padded count, not the content count.
Around 10% on a glued spine, and never less than 1 mm. A spine that is slightly too wide is far more forgiving than one that is too narrow: artwork can be extended into the wrap, but it cannot be recovered once it has been trimmed away.