Octagon Side Length in a Square

s = \frac{w}{1 + \sqrt{2}}

$s = w / (1 + sqrt(2))$

(w) Width of the Square (box)

$(w)"Width of the Square (box)"$

The Math / Science

A regular octagon is an eight sided polygon where all of the lengths of the sides and the interior angles are the same. Octagon shapes are used in many application and even in nature. Octagon shapes provide conveniences of straight sides with the general appearance of a more circular polygon.

The formula for the length of a side of a regular octagon that fits in a box is:

$s = \frac{w}{1 + \sqrt{2}}$ $s = w / (1 + sqrt(2))$

where:
s - side length
w - width of the square

Octagon Information

An octagon is a polygon with eight sides. It is a geometric shape characterized by having eight straight sides of equal length and eight angles, each measuring 135 degrees. The sum of the interior angles of an octagon is 1080 degrees. Octagons can come in various sizes and proportions but maintain the essential characteristic of eight sides. Regular octagons have all sides and angles equal, while irregular octagons can have sides and angles of different lengths and measures. Octagons are commonly encountered in geometry and can be found in various contexts, such as in the design of stop signs, certain architectural elements, and decorative patterns.

Octagon Calculators

Octagon Area: Area of regular octagon from side length.
Octagon Side from Area: Side length of octagon from area.
Octagon Radius from Area: Radius of octagon from its area.
Octagon Radius from Side Length: Length of octagon side base on the outer radius.
Octagon Side Length in a Square: Length of octagon side based on the width of the box or square containing it.
Octagon Volume: Volume of a column based on side length and height.
Octagon Column Surface Area: Surface area of column based on side length and height.
Octagon Column Mass: Mass or weight of column based on side length, height and density.
Octagon Planter Volume: Volume of soil and planting surface area in an octagon shaped planter based on dimensions.

Related Geometry Calculators

Area of a Circle - Multiple functions to compute the area of a circle or portions of a circle.
Area of Triangle - Three Sides
Area of Quadrilateral - Four Sides
Area of Pentagon - Five Sides
Area of Hexagon - Six Sides
Area of Heptagon - Seven Sides
Area of Octagon - Eight Sides
Area of Nonagon - Nine Sides
Area of Decagon - Ten Sides
Area of Hendecagon - Eleven Sides
Area of Dodecagon - Twelve Sides
Area of Polygon - Any number of sides (n).