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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, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Symmetric Pentagon, Concave Pentagon, Parallelogon, Arrow-Hexagon, Sharp Kink, Frame, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Cross, 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, Polycircle, Oval, Lemniscate, Squircle
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

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

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

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, Half Cuboid, Skewed Cuboid, Skewed Three-Edged Prism, Truncated Rhombohedron, Hollow Cuboid, Hollow Pyramid, 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, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids
4D Tesseract, Hypersphere


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Logarithmic Spiral Calculator

Calculations in a logarithmic spiral. With this form of spirals, the radius increases proportionally with the spiral length. So the distance between two turnings increases with each turning for the factor f. The shape parameter determines the spiral's shape, this value mostly if far less than 1. It is easier to use the growth factor instead. The distance from the spiral start to the origin matches the size parameter a. Enter radius, number of revolutions or angle and shape parameter or growth factor. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units.


Jacob Bernoulli, painted by Niklaus Bernoulli Spiral radius (r): Logarithmic Spiral with k = 0,19
A logarithmic spiral with 3 turnings and k = 0,19.
Number of turnings (n):
Angle (φ):
Shape parameter k:
Growth factor f:
Size parameter a:
Spiral length (l):
Outer perimeter (p):
Diameter (d):
Height (h):
Osculating radius (ρ):
Area (A):
Round to    decimal places.



Formulas:
r = a * ek*φ
n = φ / 360°
f = ( e )k
l = ( r - a ) / sin( arctan(k) )
p = l + r for n≤1
p = r - a * ek*(φ-360°) + l - ( a * ek*(φ-360°) - a ) / sin( arctan(k) ) for n>1
d = r + a * ek*(φ-180°) for φ>180°
h = a * ( ek*(φ-90°) + ek*(φ-270°) ) für φ>270°
ρ = r / cos( arctan(k) )
A = ( r² - a² ) / (4k)

pi:
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, the shape parameter and the growth factor are dimensionless.




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