Remember that when atoms form covalent bonds they share electrons. Since the electrons are the "outside" of the atom, and bonding changes the shape of an atom's orbitals (the paths the electrons are most likely to be found near), atoms may change size when they form bonds.
Atomic radius is for an unbonded carbon atom all by itself. The covalent radius is the estimated radius of that same atom when it is covalently bonded to something else. In theory, the sum of the covalent radii should equal the covalent bond length.
Atomic radius is smallest at the far right of the periodic table (O and F), and increases as you move left (towards Be and Li). Atomic radius also increases as you move down the periodic table (from F to At, for example).
The largest elements on the periodic table are Francium, Radium and Cesium (bottom left of the periodic table).
With this in mind, potassium and calcium are in the same period (horizontal row). Potassium is farther to the left than calcium is. Therefore potassium has a larger atomic radius!
Covalent radius is the radius that an atom exhibits in forming a covalent bond. It is determined by taking a number of covalently bound bonds and dividing the bond in half and then averaging them over a number of cases. Thus O= O is not the same as HO-OH for oxygen; one a double and one a single covalent bond