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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, 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, Star of Lakshmi

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Round Corner, Annulus, Annulus Sector, Ellipse, Stadium, Digon, Spherical Triangle, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, 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, 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, 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, Spherical Shell, Cylindrical Shell, Spherical Ring, Reuleaux-Tetrahedron, Torus, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


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Lens Calculator

Calculations in a convex spherical lens. This is made of two spherical caps, in between a cylinder. Those three have equal sized circular areas with the radius rc. The focal length of a lense depends on its refractive index, which is determined by its material. Here, 1.5 is set, the value for normal glass. Enter both sphere radiuses and the cylinder radius and choose the number of decimal places. Then click Calculate. The cylinder height can also be 0.


Galileo Galilei, by Justus Sustermans Radius first sphere (r1): Lens
Radius second sphere (r2):
Cylinder radius (rc):
Cylinder height (hc):
Refractive index (n):
Height of the first spherical cap (h1):
Height of the second spherical cap (h2):
Height of the lense (h):
Focal length (f):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.



Formulas:
h1 = ( 2 * r1 - √ 4r1² - 4rc² ) / 2
h2 = ( 2 * r2 - √ 4r2² - 4rc² ) / 2
h = h1 + h2 + hc
f = 1 / { (n-1) * [ 1/r1 + 1/r2 - h*(n-1)/(n*r1*r2) ] }
A = 2 * π * ( r1 * h1 + r2 * h2 + rc * hc )
V = π/3 * [ h1² * ( 3 * r1 - h1 ) + h2² * ( 3 * r2 - h2 ) ] + π * rc² * hc

The refractive index has no unit, radius, heights and focal length have the same unit (e.g. centimeter), the area has this unit squared (e.g. square centimeter), the volume has this unit to the power of three (e.g. cubic centimeter). A/V has this unit -1.




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