Theory predicts that electron pairs, which are emitted from a crystalline surface upon impact of spin-polarized low-energy electrons, can be spin-entangled. We quantify this entanglement by the von Neumann entropy, which we show to be closely related to the spin polarization of the emitted electrons. Measurement of the spin polarization therefore facilitates an experimental study of the entanglement. As target we used a Cu(111) surface, which exhibits an electronic surface state giving rise to a high pair emission intensity. Experimental spin polarization spectra for several orientations of the reaction plane broadly agree with their theoretical counterparts. They are consistent with spin entanglement of the electron pair at a macroscopic distance.