Octagon Side Length from Radius

The Octagon Side Length from Radius calculator computes the sides of length (s) of a regular octagon based on the radius.

INSTRUCTIONS:  Choose units and enter the following:

• (r) This is the radius of the octagon

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

Octagon Calculators

• Area of an Octagon from its Side Length
• Length of a side of an Octagon from its Area
• Radius of an Octagon from its Area
• Radius of an Octagon from its Side Length
• Volume of an Octagon shaped column
• Surface Area of an Octagon Column
• Mass or Weight of and Octagon Column

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.          Raised Octagon Garden

The formula for the length of a side of a regular octagon based on the radius is:

     `s = r / sqrt(  1 + 1/sqrt(2) )`

where:
s - side length
r - radius of octagon

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.