Octagon Radius from Side Length

The Octagon Radius calculator computes the radius of a circle (r) that goes around a regular octagon with sides of length (s).

INSTRUCTIONS:  Choose units and enter the following:

• (s) This is the length of one side of the 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 radius of an octagon base on the length of the sides is:

     `r = s * sqrt(  1 + 1/sqrt(2) )`

where:

• r - outer radius of octagon
• s - side length

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).

General Information

 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.          Raised Octagon Garden

Octagon Garden

How to layout the sides of an Octagon Garden:

1. Locate the center of the garden, and drive a stake in the ground.  You will need this location.
2. Cut 9 stakes.  One for the center of the octagon garden and one for each outer corner.
3. Choose 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.
4. Compute the radius of the circle around the octagon around the stake with this calculator.
5. Tie a rope around the center stake and cut or put a knot or mark on the far end to show the radius (r)
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.