Miter Angle For a 8 Sided Box

22.5° is the miter angle for a regular octagonal box — porch-post caps, planter boxes and stop-chamfer layouts all use this figure, and it's the largest side count in the common set that most compound miter saws have a built-in positive-stop detent for.

Why this one specifically

Octagons are the workhorse "many-sided" shape in construction and furniture alike, precisely because that detent exists: you can set 22.5° by feel, snapping the saw into its stop, without reading the angle scale at all. That convenience is also where the real risk hides. An 8-sided box has sixteen individual miter cuts closing the loop (two per corner), and a detent that's drifted even a tenth of a degree out of true — common on saws that get bumped or dropped — compounds silently across all sixteen before it shows up as a visible gap at the last joint. Round shapes with fewer sides (a hexagon, say) hide the same drift more easily because there are fewer cuts for it to accumulate across.

What moves the number

Purely geometric — species and stock thickness don't enter into it. What does matter is checking the saw's actual detent against a digital angle gauge periodically rather than trusting the stop blindly, especially before starting a project with this many cumulative joints.