Rg Calculator for SAS

Select first the geometrical shape and then the lengths of the semi-axes in the x-, y- and z-directions (rx,ry,rz). The values of the radius of gyration Rg, of the volume V (or area or length) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary and in metric dimensions (in small-angle scattering (SAS) usually in Å or nm). For a (double)hemisphere or a (double)cone the symmetric cut is done in the xy-plane, for a (double)semicylinder in the yz-plane, for a ring-semitorus in the torus plane (rx), for a semiring-torus normal to the torus plane (ry). In case of shapes extending infinitely in the 3rd dimension Rg of the cross-section (circle, ellipse or rectangle, rz is set to 0), and in case of shapes spreading infinitely in two dimensions Rg of the thickness (line, rx and ry are set to 0) will be calculated, respectively.

ellipsoid (rx,ry,rz), cube (rx=a/2,ry=b/2,rz=c/2), cylinder (rx,ry,rz=c/2=h/2)
bi-(<>)cone (rx,ry,rz=c/2), double-(x)cone (rx,ry,rz=c/2)
double-(x)hemisphere (rx,ry,rz=c/2), double-(x)semicylinder (rx,ry,rz=c/2=h/2)
cone (rx,ry,rz=c=h), hemisphere (rx,ry,rz=c=h)
semicylinder (rx,ry,rz=c/2=h/2), semicone (rx,ry,rz=c=h)
ring-torus (cross-section: (o)circular or (#)rectangular (a/2, b/2)
with rx: parallel to torus, ry: normal to torus; rz=c/2: radius of torus)
ring-semitorus (rx=a/2,ry=b/2), semiring-torus (rx=a/2,ry=b/2)
ellipse (rx,ry,rz=0), rectangle (rx=a/2,ry=b/2,rz=0), line (rx=ry=0,rz=c/2)

rx : ry : rz :