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

  1D Line
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, Quadrilateral, Rectangle, Rhombus, Parallelogram, Half Square Kite, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Antiparallelogram, House-Shape, Symmetric Pentagon, Concave Pentagon, Parallelogon, Stretched Hexagon, Arrow-Hexagon, L-Shape, Sharp Kink, Truncated Square, Frame, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Cross, Oktagram, Star of Lakshmi, Polygram, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Circular Corner, Crescent, Pointed Oval, Lancet Arch, Knoll, Annulus, Annulus Sector, Curved Rectangle, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Elliptical Ring, Stadium, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Tricorn, Arbelos, Salinon, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, 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, Elongated Bipyramids, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

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

Round Forms:
Sphere, Hemisphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Bicone, Truncated Bicone, Rounded Cone, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Conical Sector, Conical Wedge, Spherical Shell, Cylindrical Shell, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Spindle Torus, Toroid, Torus Sector, Toroid Sector, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids
4D Tesseract, Hypersphere


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Ellipse Calculator

Calculations in an ellipse. Enter the two semi axes and choose the number of decimal places. Then click Calculate. The semi-major axis is the distance between center and one point on the ellipse furthest away from this. The semi-minor axis is the distance between center and one point on the ellipse closest to this. They are upright to each other. The linear eccentricity is the distance of the focal points to the center. The circumference is calculated with an approximation formula (second approximation of Srinivasa Ramanujan), which is very exact up to ε<0.9 and has a maximal error of 0.04% at ε=1. An exact calculation can be done with elliptic integrals (Jacobi integrals), whose values can be taken from tables.


Srinivasa Ramanujan Semi-major axis (a): Ellipse
Semi-minor axis (b):
Axial ratio (a/b):
Linear eccentricity (e):
Numerical eccentricity (ε):
Circumference (c):
Area (A):
Round to    decimal places.



Ellipse shape:
Formulas:
e = √a² - b²
ε = e / a
c ≈ π * (a+b) * [ 1 + 3λ² / (10+√4-3λ² ) ]
λ = ( a - b ) / ( a + b )
A = π * a * b

pi:
π = 3.141592653589793...

Semi axes, linear eccentricity and circumference have the same unit (e.g. meter), the area has this unit squared (e.g. square meter). Numerical eccentricity is dimensionless.




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