The electrical properties of aerosol particles depend on their capacitance and their spatial charge distribution. A theory has been developed for the calculation of the capacitance of agglomerates of spherical components of any geometry, and any size or range of sizes. The calculations have been compared with direct measurements of capacitance made on large-scale simulations of aerosols, composed of steel spheres stuck together. In all cases, theory and experiment agree closely, and part of any discrepancy is experimental error. The theory also gives rise to the spatial distribution of electric charge, which allows equipotential surfaces to be plotted, and which enables estimates to be made of the charge that can be held before dielectric breakdown occurs.