Find each regular polygon interior angle, angle sum, diagonals, perimeter, and area quickly. Solve geometry steps with clear results and export tools.
| Polygon | Sides | Each Interior Angle | Exterior Angle | Sum of Interior Angles |
|---|---|---|---|---|
| Triangle | 3 | 60° | 120° | 180° |
| Square | 4 | 90° | 90° | 360° |
| Pentagon | 5 | 108° | 72° | 540° |
| Hexagon | 6 | 120° | 60° | 720° |
| Octagon | 8 | 135° | 45° | 1080° |
Each interior angle: ((n - 2) × 180) ÷ n
Sum of interior angles: (n - 2) × 180
Exterior angle: 360 ÷ n
Central angle: 360 ÷ n
Diagonals: n(n - 3) ÷ 2
Perimeter: n × side length
Apothem: side length ÷ (2 × tan(π ÷ n))
Circumradius: side length ÷ (2 × sin(π ÷ n))
Area: n × side length² ÷ (4 × tan(π ÷ n))
Enter the number of sides for the regular polygon.
Add a side length if you also want perimeter, area, apothem, and circumradius.
Type a unit label such as cm, m, ft, or in.
Press the calculate button.
View the result shown above the form.
Use the export buttons to save the result as CSV or PDF.
A regular polygon has equal sides and equal angles. This makes its geometry predictable. Students, teachers, designers, and exam candidates often need quick angle values. This calculator gives them without long manual work.
The main result is the interior angle of a regular polygon. It also shows the angle sum. That is useful in geometry practice. The tool can also return the exterior angle and central angle. These values help when drawing shapes, solving proofs, and checking constructions.
This calculator also finds diagonals and triangles from one vertex. Those outputs support pattern recognition in mathematics. When side length is entered, the calculator expands further. It finds perimeter, apothem, circumradius, and area. This makes the page useful for both angle work and shape measurement.
The formula starts with the sum of interior angles. For any polygon, the sum is found by subtracting two from the number of sides and multiplying by one hundred eighty. A regular polygon splits that sum evenly across all vertices. That gives the size of each interior angle.
Math learners use this tool for homework and revision. Teachers use it for classroom examples. Architects and artists use polygon angles while planning layouts and patterns. Competitive exam students use it for quick checks. It also helps in coding tasks that involve graphics or geometric modeling.
Regular polygons appear in tiles, signs, logos, engineering sketches, and digital design. Their symmetry makes them important. Understanding their angles builds strong geometry skills. It also helps with trigonometry, mensuration, and coordinate geometry.
The result section appears above the form after submission. That saves scrolling and speeds review. CSV export helps store values in spreadsheets. PDF export helps create printable records. The layout stays easy on mobile, tablet, and desktop screens.
It is the angle formed inside the polygon at each vertex. In a regular polygon, every interior angle has the same value because all sides and angles are equal.
Use this formula: ((n - 2) × 180) ÷ n. Here, n is the number of sides. The formula gives the angle in degrees for each corner of a regular polygon.
The sum is found with (n - 2) × 180. This works for any polygon. For example, a hexagon has a total interior angle sum of 720 degrees.
Interior angles are inside the polygon. Exterior angles are outside, formed by extending one side. In a regular polygon, each exterior angle equals 360 divided by the number of sides.
Yes. Enter a side length. The calculator can then estimate perimeter, apothem, circumradius, and area for a regular polygon using standard geometric formulas.
This calculator works with regular polygons only. A regular triangle is an equilateral triangle, so all three interior angles are equal. Each one is 60 degrees.
Yes. Side length accepts decimal values. That helps when working with measured shapes, design dimensions, or engineering sketches that do not use whole numbers.
A polygon must have at least 3 sides. That is why the calculator requires a whole number starting from 3 or higher.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.