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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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Pentagon Calculator

Calculations in a regular pentagon (5 vertices). Enter one value and choose the number of decimal places. Then click Calculate.


Euclid Edge length (a): Regular pentagon
Diagonal (d):
Height (h):
Perimeter (p):
Area (A):
Circumcircle radius (rc):
Incircle radius (ri):
Round to    decimal places.



Formulas:
d = a / 2 * ( 1 + √5 )
h = a / 2 * √ 5 + 2 * √5
p = 5 * a
A = a² / 4 * √ 25 + 10 * √5
rc = a / 10 * √ 50 + 10 * √5
ri = a / 10 * √ 25 + 10 * √5
Angle: 108°
5 diagonals

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

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Heights, bisecting lines and median lines coincide, these intersect at the centroid, which is also circumcircle and incircle center. To this point, the regular pentagon is rotationally symmetric at a rotation of 72° or multiples of this. Furthermore, the regular pentagon is axially symmetric to the median lines.

Pentagon, perimeter and area
perimeter p, area A
Pentagon, sides and angles
sides and angles
Pentagon, diagonals
the diagonals form a pentagram

Pentagon, height
height
Pentagon, bisecting lines
bisecting lines, interior angles 72°
Pentagon, incircle and circumcircle
incircle and circumcircle



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