Octagon Dimensions Calculator

Across flats is the perpendicular distance between two opposite parallel sides. It equals 2 x apothem = s x (1 + sqrt(2)), approximately 2.414 x s. For side 5: across flats = 12.07 units. This is the wrench size needed for an octagonal bolt head.

Across corners is the distance between two opposite vertices (the longest diagonal). It equals 2 x circumradius = s / sin(22.5), approximately 2.613 x s. For side 5: across corners = 13.07 units.

The apothem is the perpendicular distance from the center to the midpoint of one side. For a regular octagon: apothem = s x (1 + sqrt(2)) / 2, approximately 1.207 x s. For side 5: apothem = 6.04. Area can also be computed as (1/2) x perimeter x apothem.

With side 4 ft: perimeter = 32 ft (total lumber for sides), across flats = 9.66 ft (interior width), across corners = 10.45 ft (diagonal measurement for checking squareness), area = 77.25 sq ft (flooring needed). Each interior angle is 135 degrees, so you need 45-degree miter cuts at each joint.

A regular octagon inscribed in a circle covers about 90% of the circle area. The across-corners dimension equals the circle diameter. Octagons are often used to approximate circles in construction because straight edges are easier to cut and join than curves.

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