The only real information we have to go on is a line by Dr. Kynes about the size of a worm's territory. From Dune:
“Big ones may control three or four hundred square kilometers. Small ones—”
According to the non-canonical Dune Encyclopedia, Arrakis has a radius of approximately 6,128 km, giving it a total surface area of 4.72×108 km2.
So, as a really rough estimate, let's make a few assumptions:
- Dr. Kynes never finished his statement, but lets say for argument that an average-sized worm's territory to be 250 square kilometres.
- Fifteen per cent of Arrakis' surface is inaccessible to worms (the Imperial Basin, the "wormline" surrounding the north pole, rock outcroppings, etc). This would leave a "worm-friendly" surface area of approximately 4.012×108 km2.
- Let's exclude altogether other stages of the worm lifecycle (sandtrout, etc), post-spice blow areas where they could be several new worms, as well as the "stunted worms" kept by the Fremen.
- We'll also ignore instances of contested territories and rare occurrences of multiple worms rampaging after shield generators and the like, and the fact that these territories are probably highly fluid and ever-changing as worms mature and move about.
Using our extremely broad reasoning, we could say that:
401,200,000 / 250 = 1,604,800 worm territories of average size.