We study size quantization effects in InAs self-assembled quantum dots (QDs) that are embedded in GaAs. Using capacitance, photoluminescence and photovoltage spectroscopy, we correlate the measured quantized level energies with the quantum dot sizes and densities obtained from transmission electron microscopy. With increasing dot size, we observe a strong redshift of the QD features in all our data. In the capacitance spectra, a band gap renormalization of the two-dimensional wetting layer system appears when the first excited QD state crosses the wetting layer ground state. The relative size dependence and absolute energetic position of the QD transitions determined with photoluminescence provide some information about the influence of lateral confinement and height of the QD.