Octagon Radius from Area

The Octagon Radius from Area calculator computes the radius of a circle (r) that goes around an octagon with an area (A).  Regular Octagon within a Circle

INSTRUCTIONS:  Choose units and enter the following:

• (A) Area of Octagon

Octagon Radius (r):  The calculator returns the radius (r) in meters.  However, this can be automatically converted to other length units (e.g. feet) via the pull-down menu.

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 = 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.

          Raised Octagon Garden

Octagon Garden

Laying out an Octagon Garden:

1. Start with the length of the sides (s) of the octagon.  A common example is an eight foot pressure-treated landscaping timber.  For an Octagon Garden, you will need 8 of them.
2. Compute the total area (A) of the octagon based on the length of the side.  In the example of 8' sides, the area is 309 square feet.
3. Use the area (A) to compute the radius of the circle around the octagon.
4. Drive a steak in the ground at the location you wish to have as the center of you Octagon Garden.
5. Take rope or twine of the length equal to the radius of the circle (r) above, and attach one end to the steak.
6. Take one of your garden timbers and place one of its end at a point at the end of the rope.
7. Leaving that end of the timber unmoved, pick up the rope or twine and the other end of the timber, and extend them both to the point where the rope is taunt, and fix the second end of the timber to a point in the ground that is also at the end of the rope.  The goal is that both ends of the timber are the same distance (r) from the center.
8. Put the end of the next landscaping timber at the end of the first, and repeat step seven.  Do this unit all eight pieces are laid in place, and you will have an octagon pattern.