Octagon Calculator
Calculate perimeter, area, apothem, circumradius, diagonals, and interior angles based on the regular octagon side length. Octagon Calculator helps students, engineers, designers, and construction professionals analyze regular octagon dimensions accurately.
Highlights
- Calculate key regular octagon dimensions from a single side length.
- Find perimeter and area in multiple metric and imperial units.
- Determine apothem, inradius, and circumradius accurately.
- Calculate short and long diagonals for design and geometry needs.
- Get interior and exterior angles, including the total interior angle sum.
Table of Contents
How Octagon Calculator Works?
The Octagon Calculator uses the side length s of a regular octagon, meaning all eight sides and all eight interior angles are equal. From this single input, it calculates the perimeter, area, apothem, inradius, circumradius, short diagonal, long diagonal, and angle measurements.
The perimeter is the sum of the eight equal sides:
The area of a regular octagon can be found by dividing it into eight congruent triangles or by using the standard side-length formula:
The apothem is the perpendicular distance from the center to the midpoint of a side. For a regular octagon, it is also the inradius, the radius of the circle tangent to all eight sides:
The circumradius is the distance from the center to any vertex, based on the circumscribed circle:
There are two diagonal lengths provided. The short diagonal joins vertices with one intermediate vertex between them, while the long diagonal joins opposite vertices through the center:
The angle formulas depend only on the number of sides, so they do not change when the side length changes.
| Output | Formula or value |
|---|---|
| Perimeter | |
| Area | |
| Apothem and inradius | |
| Interior angle | 135° |
| Exterior angle | 45° |
| Interior angle sum | 1080° |
Enter a positive side length in any of the calculator's supported length units. Length outputs use the selected length unit, area uses the corresponding squared unit, and angular outputs are reported in degrees.
Practical Use Cases
Students: Students can use the calculator to verify geometry exercises involving regular polygons, compare perimeter and area formulas, and explore how changing the side length affects the octagon's dimensions.
Engineers: Engineers can estimate the perimeter, enclosed area, radii, and diagonal clearances of regular octagonal components during preliminary design and dimensional analysis.
Designers: Designers can determine the overall proportions of octagonal logos, platforms, layouts, furniture elements, and decorative patterns from a known side length.
Construction professionals: Construction professionals can calculate boundary length, usable floor area, center-to-edge distances, and maximum vertex-to-vertex spans for regular octagonal rooms, slabs, patios, and structures.
Fabricators: Fabricators can use the diagonal and radius results to check cut layouts, material sizing, and fit between an octagonal part and its surrounding circular or square reference geometry.
Accuracy and Limitations
The calculator uses exact regular-octagon formulas and evaluates square roots using standard numerical precision, so results are highly accurate before display rounding. It assumes the octagon is perfectly regular, with eight equal straight sides and a common center; it does not model irregular shapes, unequal sides, corner rounding, material thickness, tolerances, or construction waste. The side length must be positive and within the supported input range of 0.0001 to 1,000,000,000, and displayed values may be rounded for readability.
Quick Examples
Example #1: Small Garden Octagon
Calculate the dimensions of a regular octagon with short sides for a garden feature or decorative layout.
Example #2: Octagonal Room Design
Determine the geometric properties of an octagonal room or platform using a medium side length.
Example #3: Industrial Octagonal Platform
Analyze a large regular octagonal platform for construction and engineering planning.
