How Omni sizes post-hole concrete
The fetched Omni post hole concrete page assumes the footing hole should be roughly three times wider than the post itself. It calculates the concrete needed by subtracting the buried post volume from the full hole volume.
Formulas from the source page
Cuboid hole = (3W x 3T x D) - (W x T x D)
Cylindrical hole = pi x D x ((3 x post diameter)^2 - post diameter^2) / 4
Source example
Omni's FAQ walks through a 4 in by 4 in post buried 3 ft deep. Following the three-times-wider rule, the concrete volume for one cuboid footing is 4,608 in^3.