Aluminum is considered to approach an "ideal" metal or free electron gas. The valence electrons move freely, as if unaffected by the presence of the metal ions. Therefore, the electron redistribution due to chemical bonding is subtle and has proven extremely difficult to determine. Experimental measurements and ab initio calculations have yielded substantially different results. We applied quantitative convergent-beam electron diffraction to aluminum to provide an experimental determination of the bonding electron distribution. Calculation of the electron distribution based on density functional theory is shown to be in close agreement. Our results yield an accurate quantitative correlation between the anisotropic elastic properties of aluminum and the bonding electron and electrostatic potential distributions.