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Regular Polygon Calculator

Compute area, perimeter, apothem, and angles of any regular polygon from 3 to 14 sides.

Regular polygon formulas

Interior angle(n − 2) × 180°n
Exterior angle360°n
Sum of interior angles(n − 2) × 180°
PerimeterP = n × s
Apothema = s2 tan(180° / n)
AreaA = ½ × P × a = n s24 tan(180° / n)
CircumradiusR = s2 sin(180° / n)

Where n = number of sides, s = side length, a = apothem (center to middle of a side)

Worked examples

  1. A regular hexagon has sides of 4 cm. Find the interior angle, apothem and area.

    1. Interior angle = 4 × 180°6 = 120°
    2. P = 6 × 4 = 24
    3. a = 42 tan 30° ≈ 3.464
    4. A = ½ × 24 × 3.464

    Answer: Angle 120°, a ≈ 3.46 cm, A ≈ 41.57 cm²

  2. What is each interior angle of a regular octagon (stop sign)?

    1. Sum = (8 − 2) × 180° = 1080°
    2. 1080° ÷ 8 = 135°

    Answer: 135°

Tips & common mistakes

  • A regular hexagon is six equilateral triangles, so its circumradius equals its side.
  • Exterior angles of any convex polygon always add up to 360°.