It will provide protection from Lightning strikes for about two screens away from placement spot. That's a 40 unit radius and 80 unit diameter horizontally/vertically, and a 28.28 unit radius and 56.56 unit diameter diagonally.
To connect protection areas with multiple Rods using simple math, players should leave 14 Pitchfork tiles between each Rod horizontally/vertically. Imagine each zone as a square of 56 units in length by width instead of a circle for easier comprehension. If each Rod is placed 14 Pitchfork tiles between one another horizontally/vertically, it will create a protection grid with minimum excess overlaps.
(See the Console/Commands page for instructions on measuring distance; distance can be measured with a Pitchfork's 4x4 dig area).
The Lightning Rod also provides a small radius of light (but not heat) after absorbing a Lightning bolt, which is just bright enough to prevent Charlie from attacking. The light lasts for a few Days and will go dark as soon as morning comes.