Demagnetization factors play an important role in micromagnetics modeling but exact solutions only exist for a limited number of particle shapes. Here we use a Fourier space based approach coupled to the concept of magnetic charges to derive analytically the demagnetization factors for shapes that are subsets of a sphere: spherical sectors and spherical caps. For the uniformly magnetized hemisphere, which is a special case of both geometries, the exact demagnetization factors are shown to be Nx=Ny=7/(9π) parallel to the bottom plane and Nz=1−14/(9π) in the direction of the dome. Additionally, we provide expressions for shape amplitudes and demagnetization fields of these objects in terms of rapidly converging series. Our work demonstrates the potential of evaluating shape amplitudes to determine demagnetization factors in certain geometries and our results may facilitate numerical simulations of, for example, ferromagnetic droplets.