Octagon Calculator
How It Works
A regular octagon has eight equal sides and eight equal angles of 135 degrees each. The area formula is A = 2(1 + sqrt 2) x s^2, approximately 4.828 x s^2. Octagons are commonly seen in stop signs, architectural designs, and decorative patterns.
The apothem (distance from center to the middle of a side) equals s(1+sqrt 2)/2. This measurement is useful for determining the octagon that fits within a given circle or for cutting octagonal shapes from square material.
To cut a regular octagon from a square, cut equal isosceles right triangles from each corner. The cut length should be s/(sqrt 2) from each corner, where s is the desired octagon side length. This practical application is common in woodworking and construction.
Frequently Asked Questions
What is the area formula for a regular octagon?
Area = 2(1+√2) × s² ≈ 4.828 × s². For a side length of 10, the area is approximately 482.8 square units.
How do I make an octagon from a square?
Cut equal right triangles from each corner of a square. If the square has side length a, the triangle leg length should be a/(2+√2) ≈ 0.293a. This produces a regular octagon with side length equal to the leg length × √2.
What is the interior angle of a regular octagon?
Each interior angle is 135 degrees. The sum of all interior angles is 1,080 degrees, calculated as (8-2) × 180°.
How many diagonals does an octagon have?
A regular octagon has 20 diagonals. These come in three different lengths depending on how many vertices they skip.