Home | 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

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

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Curved Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Stadium, Digon, Spherical Triangle, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Arbelos, Salinon, Lune, Three Circles, Oval, 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, Snub Cube

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

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

Other Polyhedrons:
Cuboid, Square Pillar, 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, Half Cuboid, Skewed Cuboid, Skewed Three-Edged Prism, Truncated Rhombohedron, Hollow Cuboid, 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, Bicone, Spheroid, Ellipsoid, Semi-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
4D Tesseract, Hypersphere


Archimedean Spiral Calculator

Calculations in an archimedean or arithmetic spiral. This is the simplest form of spirals, where the radius increases proportionally with the angle. The radius is the distance from the center to the end of the spiral. Enter radius and number of turnings or angle. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units. The surface area of the archimedean spiral can only be calculated if the number of turnings is an integer.

Archimedes Spiral radius (r): Archimedean Spiral
An archimedean spiral with 3 turnings.
Number of turnings (n):
Angle (φ):
Size parameter a:
Radius of one turning (r1):
Spiral length (l):
Outer perimeter (p):
Diameter (d):
Curvature at the spiral end (κ):
Area (A):
Round to    decimal places.

r = a * φ
n = φ / 360°
r1 = a * 360° = r / n
l = a / 2 * [ φ * √ 1 + φ² + ln( φ + √ 1 + φ² ) ]
p = l(φ) + r for n≤1
p = l(φ) - l(φ-360°) + r1 for n>1
d = a * φ + a * (φ-180°) for φ>180°
κ = ( φ² + 2) / [ a * ( φ² + 1)3/2 ]
A = 4/3 π³ a² + Σ 8 ( i - 1 ) π³ a²
Σ is the sum symbol, ln is the logarithmus naturalis (natural logarithm).

π = 3.141592653589793...

Radius, parameter a, length, perimeter and diameter have a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter). The number of turnings is dimensionless. The unit of the curvature is 1 / length unit.



© Webprojects



↑ up