Geometry | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner, Formen

1DLine, Circular Arc, Parabola, Helix, Koch Curve
2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, N-gon, Polygon Ring

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, 1/2 EL Triangle, Quadrilateral, Rectangle, Golden Rectangle, Rhombus, Parallelogram, Kite, 60-90-120 Kite, Half Square Kite, Right Kite, Trapezoid, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Obtuse Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Diagonally Bisected Octagon, Cut Rectangle, Concave Pentagon, Concave Regular Pentagon, Stretched Pentagon, Straight Bisected Octagon, Stretched Hexagon, Symmetric Hexagon, Semi-regular Hexagon, Parallelogon, Concave Hexagon, Arrow-Hexagon, Rectangular Hexagon, L-Shape, Sharp Kink, T-Shape, Square Heptagon, Truncated Square, Stretched Octagon, Frame, Open Frame, Grid, Cross, X-Shape, H-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, The Hat, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Circular Central Segment, Round Corner, Circular Corner, Circle Tangent Arrow, Drop Shape, Crescent, Pointed Oval, Two Circles, Lancet Arch, Knoll, Annulus, Semi-Annulus, Annulus Sector, Annulus Segment, Cash, Curved Rectangle, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Elliptical Ring, Stadium, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Double Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Heart, Tricorn, Interarc Triangle, Circular Arc Triangle, Interarc Quadrangle, Intercircle Quadrangle, Circular Arc Quadrangle, Circular Arc Polygon, Claw, Half Yin-Yang, Arbelos, Salinon, Bulge, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, Circular Square, Digon, Spherical Triangle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Truncated Cuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron, Snub Cube, Rhombicosidodecahedron, Truncated Icosidodecahedron, Snub Dodecahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Triakis Octahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Hexakis Octahedron, Rhombic Triacontahedron, Triakis Icosahedron, Pentakis Dodecahedron, Pentagonal Icositetrahedron, Deltoidal Hexecontahedron, Hexakis Icosahedron, Pentagonal Hexecontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Gyroelongated Pyramids, Bipyramids, Elongated Bipyramids, Gyroelongated Square Dipyramid, Gyrobifastigium, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

Other Polyhedrons:
Cuboid, Square Pillar, Triangular Pyramid, Square Pyramid, Regular Pyramid, Pyramid, Square Frustum, Regular Frustum, Frustum, Bent Pyramid, Regular Bipyramid, Bipyramid, Bifrustum, Frustum-Pyramid, Ramp, Right Wedge, Wedge, Half Tetrahedron, Rhombohedron, Parallelepiped, Regular Prism, Prism, Oblique Prism, Anticube, Antiprism, Prismatoid, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Wedge-Cuboid, Half Cuboid, Skewed Cuboid, Ingot, Skewed Three-Edged Prism, Cut Cuboid, Truncated Cuboid, Obtuse Edged Cuboid, Elongated Dodecahedron, Truncated Rhombohedron, Obelisk, Bent Cuboid, Hollow Cuboid, Hollow Pyramid, Hollow Frustum, Star Pyramid, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Great Dodecahedron, Great Icosahedron

Round Forms:
Sphere, Hemisphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Bent Cylinder, Elliptic Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Truncated Elliptic Cone, General Cone, General Truncated Cone, Bicone, Truncated Bicone, Pointed Pillar, Rounded Cone, Drop, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Central Segment, Double Calotte, Double Sphere, Spherical Wedge, Half Cylinder, Diagonally Halved Cylinder, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Half Cone, Conical Sector, Conical Wedge, Spherical Shell, Half Spherical Shell, Spherical Shell Cap, Cylindrical Shell, Cut Cylindrical Shell, Oblique Cylindrical Shell, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Spindle Torus, Toroid, Torus Sector, Toroid Sector, Arch, Reuleaux-Tetrahedron, Capsule, Capsule Segment, Double Point, Anticone, Truncated Anticone, Sphere-Cylinder, Lens, Concave Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids, Solid of Revolution
4D Tesseract, Hypersphere


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Regular N-gon Calculator

Calculations at a regular n-gon or regular polygon.
Enter edge length and number of vertices and choose the number of decimal places. Then click Calculate. The length of a diagonal across a number of edges can also be calculated. Angles are calculated and displayed in degrees, here you can convert angle units.


Euclid Edge length (a): N-gon
Example: tridecagon
Number of vertices (n):
Perimeter (p):
Height (h):
Area (A):
Circumcircle radius (rc):
Incircle radius (ri):
Angle:
Number of diagonals d:
Diagonals across edges (dm):
Round to    decimal places.



Regular n-gon shape (up to 100 vertices):
Formulas:
n ∈ ℕ, n > 2
p = a * n
h = 2 * ri   if n is even, else
h = a / ( 2 * tan( π/2/n ) )
A = n * a² / ( 4 * tan(π/n) )
rc = a / ( 2 * sin(π/n) )
ri = a / ( 2 * tan(π/n) )
Angle = 180° - 360° / n
d = n ( n - 3 ) / 2

Diagonal across m edges, m∈ℕ, m≤n/2:
dm = a * sin( π * m/n ) / sin( π/n )

π = 180° = 3.141592653589793...

Edge length, diagonal, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Another name for the regular polygon is equilateral and equiangular polygon. With an increasing number of corners and sides, it gets closer and closer to the circle and the incircle and circumcircle get closer and closer to each other. With an infinite number of sides, the circle, polygon, incircle and circumcircle are ultimately identical. The length of the sides becomes smaller and smaller as the number increases with the same radius, but with decreasing dimensions. The equilateral triangle is therefore the furthest away from the circle. The most famous is the regular quadrilateral, better known as square.
The regular polygon is point-symmetrical to its center. It is axially symmetric about every perpendicular bisector with an odd number of vertices and with an even number of vertices additionally axially symmetric about every diagonal between two opposite vertices. Therefore, equilateral polygons with n vertices have n axes of symmetry. Rotational symmetry number is identical to the number of corners.
If you remove a similar but smaller polygon from the middle of a regular polygon, you get a polygon ring. The three-dimensional equivalent of regular polygons are regular polyhedra. There are an infinite number of such polygons, but only five polyhedra, the Platonic solids.



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