Polygon Calculator

Calculate properties of a regular polygon from the number of sides and the side length.

Last updated: June 2026 | By Patchworkr Team

Regular Polygon

Number of Sides

Side Length

Math check: area = n s^2 / (4 tan(pi / n))

Result

PolygonHexagon

Perimeter30

Area64.951905

Interior Angle120 deg

Exterior Angle60 deg

Apothem4.330127

Circumradius5

Diagonals9

Formula

interior angle = (n - 2) * 180 / n

exterior angle = 360 / n

area = n s^2 / (4 tan(pi / n))

diagonals = n(n - 3) / 2

For 8 sides of length 4, the polygon is an octagon, and the formulas produce the area, perimeter, and angle values.

The number of diagonals is 8(8 - 3) / 2 = 20.

This calculator is for regular polygons only. Irregular polygons need coordinate-based methods like the shoelace formula.

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