In this work, we present a new formula for evaluating the half-power beamwidth (HPBW) of 1-D leaky-wave antennas (1-D LWAs). With respect to Oliner's formula, whose validity is restricted to certain hypothesis on the beam size and the pointing angle, our analysis is quite general, being accurate even when radiation points near endfire, where current formulas notably diverge. Even more interestingly, this new expression takes into account the dependence of the HPBW on different parameters, namely the length of the antenna, the pointing angle, and the attenuation constant. A simple approximate analytical formula is derived and validated through numerical results. To complete the picture, previous Oliner's formula is obtained as a limiting case of this general formulation. These results would provide a very useful tool for the correct prediction of the radiating features of 1-D LWAs.