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Home | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner

2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, N-gon

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Oktagram, Star of Lakshmi, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

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

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid

Other Polyhedrons:
Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Skewed Cuboid, Truncated Rhombohedron, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron

Round Forms:
Sphere, Hemisphere, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


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Polygon Calculator

Calculations in a simple polygon. A polygon consists of straight edges and at least three vertices. It is simple when the edges don't intersect, so if the polygon isn't crossed. Here the edge lengths as well as the perimeter and area of the polygon can be calculated from the cartesian coordinates. First enter the number of vertices (3 to 30), then the x- and y-coordinate of each vertex. Choose the number of decimal places, then click Calculate. Side 1 runs from vertex 1 to vertex 2, side 2 from vertex 2 to 3, ..., the last side runs from vertex n to 1.


Carl Friedrich Gauß, by Gottlieb Biermann Verices (n): Simple Polygon
A simple polygon with 14 vertices.
Vertex  1: x= y=
Vertex  2: x= y=
Vertex  3: x= y=
Vertex  4: x= y=
Vertex  5: x= y=
Round to    decimal places.

 

Edge 1:
Edge 2:
Edge 3:
Edge 4:
Edge 5:
Perimeter (p):
Area (A):

Polygon shape. If this polygon is drawn crossed, then the upper area calculation is incorrect:
Formulas:
Length of edge i = √ ( xi+1 - xi )² + ( yi+1 - yi
  n
p = Σ ( xi+1 - xi )² + ( yi+1 - yi
 i=1
  n
A = |   Σ xi * yi+1 - yi * xi+1 | / 2
 i=1
with xn+1 → x1 and yn+1 → y1

Σ is the sum symbol, | | is the absolute value.

x- and y-coordinate determine the position of a point right from and above the origin in the cartesian coordinate system. Edge lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).




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