The magnetic phase diagram of erbium with a magnetic field applied along the hexagonal c axis has been investigated using high-resolution neutron diffraction. The authors find that there are three distinct ordered phases occupying different regions of the field-temperature plane, a cone phase is found at high fields (B>or=2 T) which has an incommensurate structure at temperatures above 40 K, but which becomes commensurate on cooling, first with a wavevector of q_m=1/4c* and then with q_m=5/21c*; a nearly cycloidal structure in fields below 2 T, with a wavevector which passes through a series of commensurate values, with those structures having a net c axis moment being particularly favoured; and a phase at temperatures above 60 K which is mostly longitudinally modulated, but which also has a smaller basal plane component with a different wavevector.