Numerical Hartree-Fock calculations have been performed with Dirichlet boundary conditions to calculate various global reactivity descriptors such as softness, electronegativity, polarizability, electrophilicity index, and mean excitation energy for several atoms (He, Li, Be, B, C, N, O, F, Ne) and ions (C+, C2+, C3+, Ca4+) confined in a spherical box. All of the systems become harder and less polarizable with a decrease in confinement volume. Electronegativity and electrophilicity are not very sensitive, except for very small cutoff radius at which they change abruptly. Mean excitation energy decreases with an increase in the box size. Linear relationship between softness and the cube-root of polarizability is observed for all of the confined atoms and ions. Scaled hardness shows opposite trends of softness, except for Li. Expected behavior is observed for the energy, virial, and various moments. With ionization, systems become more electronegative, harder, and less polarizable at all sizes.