The mathematically calculated atomic radius of fluorine is 42 picometers (10^-12 meters) while the experimentally measured value is about 50 picometers.
The atomic radius of a chemical element is defined as the distance between the center of the nucleus and the outermost shell of electrons surrounding that nucleus. Although the surrounding electron cloud is not truly spherically shaped, it can be thought of as a sphere for the purposes of this measurement, thus making the measurement the radius of a sphere. Also, the positions of the electrons are constantly changing, so there is no hard, constant value for this measurement.
In general, atomic radii tend to increase as you move down a group (vertical row) due to the increase in atomic shells and decrease as you move across a period (horizontal row) due to the increased attraction of the electrons with a larger nucleus. That makes hydrogen and helium the elements with the smallest atomic radii. But since fluorine sits in the upper right hand corner of the periodic table, that means that it too has amongst the smallest of atomic radii.
The atomic radius for flourine is 42 picometers which is 42 * 10^(-12) meters.