  We calculate the number of open walks of fixed length and algebraic area on a
square planar lattice by an extension of the operator method used for the
enumeration of closed walks. The open walk area is defined by closing the walks
with a straight line across their endpoints and can assume half-integer values
in lattice cell units. We also derive the length and area counting of walks
with endpoints on specific straight lines and outline an approach for dealing
with walks with fully fixed endpoints.
