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Atomic radius applies to a single atom. It is the distance from the center of the nucleus to the boundary of its electron cloud. Covalent radius applies when two atoms of the same species are bonded. It is half of the distance between the two nuclei.
When you have a covalent bond between atoms you can find the covalent radius. The distance between the two nuclei of the atoms will give you the diameter so you would have to divide by two. Atomic radius is just focusing on one atom.
Another important note here is that a covalent bond is the sharing of electrons. So when two atoms are covalently bonded, their closeness to one another is because they are sharing electrons, which contribute to their radii. So there may be a sort of "overlap" of those outer valence shells. So an atom's atomic radius is going to be larger than it's covalent radius, because the covalent radius is half of the distance between the two atoms' centers, and those centers are closer because of the sharing nature of the covalent bond.
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