Partial core corrections can be important in obtaining an accurate description of nonlinear exchange-correlation functionals and improving the transferability of pseudopotentials. We show that a widely used procedure, which calculates partial core charge density, ρ core partial, in Fourier space and then converts it to real space with fast Fourier transforms, can lead to sizable numerical errors of exchange-correlation potentials in the vacuum region. Such errors occur in modeling low-dimensional materials or surfaces with supercells. The loss of accuracy originates from the slow-decaying feature of core charge density in reciprocal space. Numerical errors on the order of 1 eV in the Kohn-Sham energies of unoccupied states can occur in pseudopotential-density functional calculations. The direct calculation of the partial core charge in real space can avoid the numerical errors caused by Fourier transforms.