Three online calculators combined into one: compute side length (x), area (A), radius of inscribed circle (r, inradius) and radius of circumscribed circle (R, circumradius) of a regular polygon. Let n be the number of sides.
Enter n (≥3) and circumradius R. Get side x, inradius r, area A.
Formulas used: For a regular polygon with \(n\) sides of length \(x\), inradius \(r\), circumradius \(R\), and area \(A\):
• \( r = \frac{x}{2} \cot\left(\frac{\pi}{n}\right) \) | \( R = \frac{x}{2} \csc\left(\frac{\pi}{n}\right) \)
• \( x = 2r \tan\left(\frac{\pi}{n}\right) = 2R \sin\left(\frac{\pi}{n}\right) \)
• \( A = \frac{1}{2} n \, x \, r = \frac{1}{2} n \, R^2 \sin\left(\frac{2\pi}{n}\right) = n \, r^2 \tan\left(\frac{\pi}{n}\right) \)
Note: n must be an integer ≥ 3. All inputs must be positive numbers.