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Octagon Calculator

Octagon calculator calculates various properties of a regular octagon, such as the inradius, circumradius, diagonals, perimeter and area.

The calculator is easy to use. Simply enter one known value and the calculator will quickly give you the results you need. The perimeter, area, length of diagonals, as well as the radius of an inscribed circle and circumscribed circle will all be available in the blink of the eyes.

What is a regular octagon? 

A regular octagon is a geometric shape with 8 equal lengths and 8 equal angles. The sum of the interior angles of a regular octagon is 1080 degrees, which makes each angle equal to 135 degrees in measure. 

Area of a regular octagon:

One can think of the regular octagon as a square with corners that have been cut off or shortened. If you label “a” as the length of one side of an octagon, then the sides of the large square are a(square root(2) +1).  From there, you can determine the area of the large square by squaring the previous result.

The area is the area of the 4 small triangles formed from the truncation of the square, subtracted off from the area of the square.

A = S - a² = (3 + 2√2)a² - a²

The perimeter is the easiest to calculate it's just the sum of the lengths of all the sides.  Therefore, the perimeter, noted with a P is P = 8a.

Suppose though that  you don't know the length of an edge, but you know the area. The perimeter is determined by the formula:

P = square root(32A/(square root(2) +1)]

Diagonals

With numerous diagonals, the task of calculating the lengths may seem daunting. First, there are three different types of diagonals., will call them “short”, “medium” (which as also known as the height of the octagon) and “long”.

The formulas for calculating the lengths are actually quite easy to use.

Short = a([square root(2)+square root(2)])

Medium = a(square root(2) + 1)

Long = a([square root(4) +2square root(2)])

Cicrumradius and inradius

Simply put, the circumradius is half of the length of the longest diagonal, whereas the inradius is half of the height of the octagon.