Valence electrons experience an electrostatic force from the nucleus. The nucleus has its character positive charge, but due to shielding by core electrons the total positive charge is not completely felt by the electrons, so the actual net positive charge felt by the valence electron has its own name and is called the effective nuclear charge $Z_{eff}$. This effective nuclear charge, largely effects the size of the atom. The general trend of the periodic table is that as you go down a group, and go from right to left, the $Z_{eff}$ decreases, and you see an increase in the size of the atom. The easy way to think of it, is that as you go from left to right, the number of valence electrons, and protons increases but the number core electrons stays the same; so, you see an increase in $Z_{eff}$.
$Z_{eff}$ is calculated using Slater's Rules. Where
$$Z_{eff}=Z-s$$
Where $Z$ is the atomic number and $s$ is the shielding constant.
The rules for calculating are as follows (from wikipedia):
Firstly,(1)(4) the electrons are arranged into a sequence of groups in order of increasing principal quantum number n, and for equal n in order of increasing azimuthal quantum number l, except that s- and p- orbitals are kept together.
$\mathrm{(1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s, 5p) (5d)}$ etc.
Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.
The shielding constant for each group is formed as the sum of the following contributions:
An amount of 0.35 from each other electron within the same group except for the (1s) group, where the other electron contributes only 0.30.
If the group is of the (s p) type, an amount of 0.85 from each electron with principal quantum number n one less than that of the group, and an amount of 1.00 for each electron with principal quantum number two or more less.
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If the group is of the (d) or (f), type, an amount of 1.00 for each electron "closer" to the atom than the group. This includes
i) electrons with a smaller principal quantum number n and
ii) electrons with an equal principal quantum number and a smaller azimuthal quantum number l.