Rg-Calculator for concentric core/shell 3D-shapes (SAS)

Core/shell 3D-shapes can be composed of up to 5 different or same (centrosymmetric) shapes with the shell's centroids in the common center of gravity. Select the geometrical shape, lengths of the axes (a,b,c), or radii (rx,ry,rz) and/or height (h) or torroidal radius (R) in the x-, y- and z-directions and the electron density (e) of each shell, with e(1) being the innermost shell and e(n) the outermost shell, respectively. The values of the radius of gyration Rg, of the total Volume times e-density (e*Vol) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

ellipsoid/sphere (rx,ry,rz)
hexahedron/tetrahedron/octahedron (rx=ry=rz=a)
cylinder (rx,ry,rz=h), bi-cone (rx,ry,rz=h)
bi-pyramid (3): (rx=a,a,ry=b,a>b/2,rz=h), prism (3): (rx=a,a,ry=b,rz=h) *(isosceles) triangular base*
bi-pyramid (4): (rx=a,ry=b,rz=h), prism (4): (rx=a,ry=b,rz=h) *rectangular base*
bi-pyramid (5,6): (rx=a,ry=a,rz=h), prism (5,6): (rx=a,ry=a,rz=h) *equilateral base*
bi-pyramid (rhombic): (rx,ry,rz=h), prism (rhombic): (rx,ry,rz=h)
torus o (elliptic): (rx,ry,rz=R), torus # (rectangular): (rx=a/2,ry=b/2,rz=R)
torus (o and #): rx: parallel to the torus plane, ry: parallel to the central torus axis



e(1): rx (a): ry (b): rz (c/h):
e(2): rx (a): ry (b): rz (c/h):
e(3): rx (a): ry (b): rz (c/h):
e(4): rx (a): ry (b): rz (c/h):
e(5): rx (a): ry (b): rz (c/h):



Radius of gyration: e*Vol: I(0):




Rg-Calculator for concentric core/shell 2D-shapes (SAS)

Core/shell 2D-shapes can be composed of up to 5 different or same (centrosymmetric) shapes with the shell's centroids in the common center of gravity. Select the geometrical shape, lengths of the axes (a,b), or radii (rx,ry) and the electron density (e) of each shell, with e(1) being the innermost shell and e(n) the outermost shell, respectively. The values of the radius of gyration Rg (2-dimensional Rg, or Rg of the cross-section), of the total Area times e-density (e*A) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

circle/ellipse: (rx,ry)
triangle (3): (rx=a,ry=b,a>b/2), rectangle (4): (rx=a,ry=b) *(non)equilateral*
pentagon (5): (rx=a,ry=a), hexagon (6): (rx=a,ry=a) *equilateral*
rhombus: (rx,ry) *(non)equilateral*



e(1): rx (a): ry (b):
e(2): rx (a): ry (b):
e(3): rx (a): ry (b):
e(4): rx (a): ry (b):
e(5): rx (a): ry (b):



Radius of gyration: e*A: I(0):



Author: M.Kriechbaum, TU-Graz (2015, 2026), e-mail: manfred.kriechbaum@tugraz.at