The radiation pattern of one-dimensional (1-D) unidirectional leaky-wave antennas (LWAs) is typically derived from the analysis of the space factor (SF) only. However, when the antenna aperture is characterized by a longitudinal radiating current, a cosine-type element pattern term has to be included: this factor may considerably affect the beam properties. Specifically, the beam peak is shifted and the beamwidth is narrowed when the element pattern is included. These effects are more prominent as the antenna size decreases and the beam angle increases. Approximate but accurate analytical formulas are here provided and numerically validated to predict the beam angle and the half-power beamwidth for these kinds of 1-D unidirectional LWAs when the element pattern is included.