There is no fitting rule here, only a convention
Ring size has a hard failure mode: too small and it will not go over the knuckle, too large and it spins. A bangle has one too: too small and it will not clear the hand at all. A watch case has neither — it sits on top of the wrist rather than around it, so nothing stops a case from being any size at all, and the question "what size fits me" is really "what looks proportionate to me", which is a matter of convention rather than physics.
The convention the trade actually uses starts from the wrist's width rather than its circumference. A wrist is roughly circular in cross-section, so its width can be estimated from a tape-measured circumference using the same relationship that links a circle's diameter to its circumference: width is approximately the circumference divided by pi. From there, the styling rule of thumb treats a case reading as balanced when its diameter falls between 60% and 75% of that estimated width — narrower than the wrist itself, but not by a huge margin.
Strap width and lug-to-lug, the parts the diameter spec hides
A case diameter on its own understates how large a watch actually reads on the wrist, because two watches with an identical diameter can have very different lug-to-lug lengths — the distance between the points where the strap attaches. A watch with lugs that extend well past the case edge will overhang a wrist that a same-diameter, compact-lugged watch sits comfortably on. The conventional soft cap here is that lug-to-lug should not exceed the flat top of the wrist, estimated as roughly the circumference divided by 2.5.
Strap width follows its own convention: roughly half the case diameter, rounded to a size straps are actually sold in. Watch straps have historically been produced in 2 millimetre increments — 18, 20, 22 and so on — so a 40 mm case conventionally pairs with a 20 mm strap rather than some intermediate figure nobody stocks.
Why deliberately ignoring this convention is common, and fine
Plenty of respected watches sit well outside the 60–75% band on purpose. Dive watches have run oversized relative to the wrist for decades, precisely because visibility and a substantial bezel matter more than proportion in that category. Dress watches trend the opposite way, favouring a slim, understated case even on a larger wrist. Neither choice is a mistake by this convention's own logic — a convention is a starting point for someone with no other preference, not a rule that overrides one.