1. What is the Polygon Side Formula?

The polygon side formula calculates the length of each side in a regular polygon given its circumradius and number of sides. A regular polygon has all sides and angles equal.

2. How Does the Calculator Work?

The calculator uses the regular polygon side formula:

Where:

• \( s \) — Side length (same units as r)
• \( r \) — Circumradius (distance from center to vertex)
• \( n \) — Number of sides (must be ≥3)

Explanation: The formula derives from dividing the regular polygon into n isosceles triangles and using trigonometric relationships.

3. Importance of Side Length Calculation

Details: Knowing side lengths is essential for constructing regular polygons, architectural design, and various engineering applications.

4. Using the Calculator

Tips: Enter the circumradius in any length units and the number of sides (integer ≥3). The result will be in the same units as the circumradius.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between circumradius and apothem?
A: Circumradius is center-to-vertex distance, while apothem is center-to-midpoint of a side.

Q2: Can this be used for irregular polygons?
A: No, this formula only works for regular polygons where all sides and angles are equal.

Q3: What's the minimum number of sides?
A: 3 (triangle). The formula works for any integer n ≥ 3.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular polygons. Real-world measurements may vary.

Q5: Can I calculate area with this?
A: Yes, once you have the side length, you can calculate area using other polygon formulas.