Calculadora de Ângulos do Polígono
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
S = (n − 2) × 180°
About this calculator
The Polygon Angle Calculator is a practical tool to determine the sum of interior angles, the interior angle, and the exterior angle of a regular polygon. Simply enter the number of sides (n) to get instant results. It is useful for students, teachers, and professionals working with geometry, architecture, or design.
The calculation of the sum of interior angles (S) uses the formula S = (n − 2) × 180°. For example, a pentagon (5 sides) has sum = (5−2)×180° = 540°. For regular polygons, the interior angle is the sum divided by the number of sides, and the exterior angle is 360° divided by n. The calculator automates these steps, avoiding manual errors.
Use this calculator in situations such as: designing furniture pieces with angular cuts, determining angles in mosaics or flooring, solving geometry problems in exams, or verifying shape feasibility in engineering projects. It is especially useful when working with polygons with many sides, where manual calculations are tedious.
Cautions: the formula assumes convex and regular polygons (all sides and angles equal). For irregular polygons, the sum of interior angles still holds, but individual angles vary. Also, ensure you use the correct number of sides; a triangle has 3 sides, not 4. The calculator does not validate if the polygon is possible (n ≥ 3).
Frequently asked questions
What is a regular polygon?
It is a polygon with all sides of equal length and all interior angles equal. Examples: equilateral triangle, square, regular pentagon.
Does the formula work for any polygon?
The sum of interior angles works for any convex polygon, but the interior and exterior angles calculated (division by n) are only valid for regular polygons.
What is the smallest number of sides a polygon can have?
The smallest number of sides is 3, forming a triangle. A polygon with 2 sides is not possible in Euclidean geometry.
How do I calculate the exterior angle manually?
The exterior angle of a regular polygon is 360° divided by the number of sides. For example, a hexagon (6 sides) has an exterior angle of 60°.
Can I use this calculator for concave polygons?
No. The formula for the sum of interior angles still applies, but interior and exterior angles are not uniform. The calculator is designed only for regular convex polygons.