Octagon Area

The Area of an Octagon calculator computes the area of a regular Octagon given the length of sides (s).  

INSTRUCTIONS:  Choose units and enter the following:

• (s) Length of One Side of the Octagon

Area of Octagon(A):  The calculator returns the area in square meters.  However, this can be automatically converted to other area units (e.g. square feet) via the pull-down menu.

The Math / Science

A regular octagon is an eight sided polygon where all of the sides are the same length and the interior angles are the same (22.5°).  The formula for the area of a regular octagon is:

      `A = 2 (1+ sqrt(2)) * s^2`

where:

• A = Area of Octagon
• s = length of one side

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.

Regular Polygon Information

A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length .  Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side.  As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.

The names of polygons vary based on the number of sides as follows:

• triangle - 3 sides
• square - 4 sides 
• pentagon - 5 sides
• hexagon - 6 sides
• heptagon - 7 sides
• octagon - 8 sides
• nonagon - 9 sides
• decagon - 10 sides
• hendecagon - 11 sides
• dodecagon - 12 sides

Common Regular Polygon Functions

Polygon Area Calculators:

• Polygon Area from the Number of sides and Length of Sides
• Polygon Area from the Number of Sides and Outside Radius
• Area of a Polygon Segment (triangle) from the Number of Sides and Inscribed Radius
• Polygon Area from the Number of Sides and Inscribed Radius.

Polygon Side Calculators

• Length of a Polygon Side from the Number of Sides and Outer Radius
• Length of a Polygon Side from the Number of Sides and Inner Radius
• Length of a Polygon Side from the Number of Sides and Area in Poloygon

Polygon Perimeter Calculators

• Perimeter of a Polygon from Number of Sides and Length of Sides
• Perimeter of a Polygon from Number of Sides and Outer Radius
• Perimeter of a Polygon from Number of Sides and Inner Radius
• Polygon Perimeter from the Area and Number of Sides

Polygon Radius

• Radius of Circle around a Polygon

3D Polygon Shapes

• Polygon Ring Volume

Other Polygon Calculators

• Interior Angle of a Regular Polygon based on the number of sides
• Area of Circle - Circle approximates a polygon as the number of sides approaches infinity.
• Area of Triangle -  Three Sides
• Area of a Square - 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