Decagon Calculator
Calculate perimeter, area, apothem, circumradius, diagonals, and angles based on the side length. Decagon Calculator helps students, designers, engineers, and educators analyze regular decagon geometry.
Highlights
- Calculate the perimeter and area of a regular decagon.
- Find the apothem and circumradius from the side length.
- Determine short, long, and maximum diagonal lengths.
- Calculate interior, exterior, and central angles.
- Get the total number of diagonals in a decagon.
Table of Contents
How Decagon Calculator Works?
The Decagon Calculator analyzes a regular decagon, which has 10 equal sides and 10 equal interior angles. Enter the side length s using a supported length unit such as mm, cm, m, in, ft, or yd. The calculator then determines the perimeter, area, radii, diagonals, and angle measurements.
The perimeter is the total length around the decagon. The apothem is the perpendicular distance from the center to the midpoint of a side, while the circumradius is the distance from the center to any vertex.
Here, a represents the apothem and R represents the circumradius. The area can be calculated by dividing the decagon into 10 congruent triangles, each with base s and height a.
Diagonal lengths come from chord lengths in the circumcircle. The short diagonal skips one vertex, the long diagonal skips two vertices, and the maximum diagonal connects opposite vertices through the center.
| Property | Formula or value |
|---|---|
| Perimeter | |
| Area | |
| Interior angle | 144° |
| Exterior angle | 36° |
| Sum of interior angles | 1,440° |
| Central angle | 36° |
| Number of diagonals |
All length outputs use the selected length unit, area uses the corresponding squared unit, and angle outputs are given in degrees.
Practical Use Cases
Students: Students can check geometry homework involving regular polygons, verify perimeter and area calculations, and compare apothems, circumradii, and diagonal lengths for different side lengths.
Teachers and educators: Educators can use the calculator to demonstrate how a regular decagon divides into 10 triangles, explain central and interior angles, and create practical examples for lessons on polygon geometry.
Designers: Designers can estimate the boundary, enclosed area, and vertex-to-vertex spans of decagonal layouts used in logos, floor patterns, decorative panels, signs, and other visual structures.
Engineers and technical planners: Engineers can obtain preliminary geometric dimensions for regular decagonal components, including the circumradius, apothem, maximum diagonal, and total perimeter needed for early-stage layouts.
Fabricators and craftspeople: Fabricators can use the side length to determine the overall outline, center-to-edge distance, and diagonal spans before marking, cutting, or assembling a regular decagonal part.
Accuracy and Limitations
The calculator uses exact regular-decagon relationships with trigonometric constants, so its results are mathematically accurate for a decagon with 10 equal sides and equal angles; displayed values may be rounded for readability. It accepts side lengths from 0.0001 to 1,000,000,000 in the selected supported length unit and requires a positive numeric input. The formulas do not apply directly to irregular decagons, whose sides or angles differ. Diagonal outputs distinguish the step-2 short diagonal, step-3 long diagonal, and step-5 maximum diagonal; they should not be interpreted as a single generic diagonal.
Quick Examples
Example #1: Small Decagon
Calculate the geometric properties of a regular decagon with a short side length.
Example #2: Garden Design Decagon
Determine the dimensions and area of a regular decagon used in a landscaping or garden layout.
Example #3: Large Industrial Decagon
Analyze the perimeter, diagonals, radii, and angles of a large regular decagon structure.
