We calculate the Lusternik–Schnirelmann category of the
kth ordered configuration spaces F(Rn,k)
of Rn and give bounds for the category of the
corresponding unordered configuration spaces B(Rn,k)
and the sectional category of the fibrations
πnk:F(Rn,k)→
B(Rn,k). We show that
secat(πnk) can be expressed in terms of
subspace category. In many cases, eg, if n is a power of 2, we
determine cat(B(Rn,k)) and
secat(πnk) precisely.