Why don't atoms have an overall charge?

Atoms are made up of three types of particles: protons, neutrons and electrons.

The relatives charge on each of these particles are as follows: protons = +1, neutrons = 0, electrons = -1

Because neutrons are not charged, they don't affect the overall charge of the atom.

The number of protons in an atom is equal to the number of electrons. Because protons and electrons have equal but opposite charges, they cancel each other out.