Regular Polygon Calculator – Guide & Formulas
Calculate the area, perimeter, interior angles, and apothem of any regular polygon with 3 to 100 sides.
Analyze any regular polygon. Input the number of sides and the side length to instantly evaluate area, perimeter, apothem, circumradius, and interior angles.
Key Takeaway
Use the free Regular Polygon Calculator to calculate the area, perimeter, interior angles, and apothem of any regular polygon with 3 to 100 sides. Get instant results with step-by-step explanations.
How to Use the Regular Polygon Calculator
- Enter the number of sides (n) of your polygon (minimum 3).
- Enter the side length of each side.
- Examine the resulting geometric breakdown, angle summaries, and apothem.
The Formula
Variable Definitions
- n: The number of sides (degree of polygon)
- s: Length of each individual side
- A: Total calculated surface area
- P: Total boundary perimeter
Sizing an Octagonal Stopping Sign
Calculate the total metal area of an 8-sided regular stop sign with 10-inch sides.
- Step 1: Set number of sides n = 8 and side length s = 10 inches.
- Step 2: Calculate perimeter: 8 * 10 = 80 inches.
- Step 3: Apply the general regular polygon formula: 0.25 * 8 * 10² / tan(180/8) ≈ 482.84 square inches.
- Step 4: The face area of the stop sign is approximately 482.84 square inches.
Frequently Asked Questions
What is a "regular" polygon?
A polygon is regular if all its sides are equal in length (equilateral) and all its interior angles are equal in measure (equiangular).
How do you find the sum of interior angles?
The sum of interior angles for any n-sided polygon is calculated as (n - 2) * 180 degrees.
What happens as the number of sides approaches infinity?
As the number of sides (n) increases towards infinity, the regular polygon's shape and area converge closer and closer to a perfect circle.