Regular polygon calculator

Calculate a regular polygon’s angles, area and diagonal count.

Angles and counts

Sides6

Vertices6

Interior angle120°(n − 2) × 180 / n

Exterior angle60°360 / n, and the exterior angles of any polygon sum to 360°

Sum of interior angles720°(n − 2) × 180

Central angle60°subtended at the centre by one side

Diagonals9n(n − 3) / 2

Triangles from one vertex4n − 2

Schläfli symbol{6}

Side length4

Perimeter24n × s

Area41.56921938≈n s² / (4 tan(π/n))

Area as a multiple of s²2.59807621 s²≈

Circumradius4≈centre to a vertex, s / (2 sin(π/n))

Inradius (apothem)3.46410162≈centre to the midpoint of a side, s / (2 tan(π/n))

Area of the circumcircle50.26548246≈

Share of its circumcircle filled82.699334%≈rises towards 100% as n increases

Rotational symmetry order6

Lines of reflection6

Symmetry groupDihedral D6, order 12

Compass and straightedgeConstructibleGauss-Wantzel: n = 2^1 × 3, a power of two times distinct Fermat primes

Tiles the plane aloneYesone of only three regular polygons that tile on their own

Interior angleθ = (n − 2) × 180 / n

Exterior anglee = 360 / n

DiagonalsD = n(n − 3) / 2

AreaA = n s² / (4 tan(π/n))

CircumradiusR = s / (2 sin(π/n))

Inradiusr = s / (2 tan(π/n))