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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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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 revolutions 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 revolutions is an integer.


Archimedes Spiral radius (r): Archimedean Spiral
An archimedean spiral with 3 revolutions.
Number of revolutions (n):
Angle (φ):
Parameter a:
Radius of one revolution (r1):
Spiral length (l):
Outer perimeter (p):
Curvature at the spiral end (κ):
Surface area (A):
Round to    decimal places.



Formulas:
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
κ = ( φ² + 2) / [ a * ( φ² + 1)3/2 ]
  n
A = 4/3 π³ a² + Σ 8 ( i - 1 ) π³ a²
 i=2
Σ is the sum symbol, ln is the logarithmus naturalis (natural logarithm).

pi:
π = 3.141592653589793...

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




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