Angle calculations are derived for the operation of a '4S+2D' six-circle X-
ray or neutron diffractometer. The six degrees of freedom [four sample-orie
nting ('4S') and two detector-orienting ('2D')] of the diffractometer are u
sed to control the scattering vector and a reference vector in the laborato
ry frame of reference. Several modes of operation unavailable in other type
s of diffractometer are presented.