Octagon Calculator

Calculate area, perimeter, diagonals, inradius, and circumradius of a regular octagon from side length.

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Result

120.71 area

Total area of a regular octagon with side length 5.

Perimeter
40
Circumradius
6.53
Inradius
6.04
Long diagonal
13.07
Medium diagonal
12.07
Short diagonal
9.24

Also in General

Geometry

Regular octagon properties from side length

The octagon calculator computes area, perimeter, diagonals, inradius, and circumradius of a regular octagon from its side length.

Octagon formulas

A regular octagon has eight equal sides and internal angles of 135 degrees. Area = 2(1 + sqrt(2)) * s^2. Perimeter = 8s.

The circumradius (centre to vertex) is s / (2 * sin(pi/8)). The inradius (centre to side midpoint) is s / (2 * tan(pi/8)).

Limitations

This calculator handles regular octagons only.

Frequently asked questions

What shape is an octagon?

An eight-sided polygon. Stop signs are the most recognisable regular octagon in daily life.

What is the interior angle of a regular octagon?

135 degrees. The formula is (n-2) * 180 / n = (8-2) * 180 / 8 = 135.

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