In this paper, a general formula for the half-power beamwidth of one-dimensional leaky-wave antennas (1-D LWAs) is presented. With respect to previous beamwidth formulas found in the literature, the new formula allows for both arbitrary propagation wavenumber and length of the antenna. The pointing angle of the beam is allowed to be arbitrary, and may be near broadside or endfire, or any angle in between. The beamwidth is also allowed to be arbitrary, though a simpler approximate expression is obtained under the assumption of a narrow beam. Numerical results confirm the accuracy of the new beamwidth formula. Furthermore, it is shown that the previous existing formulas are approximate limiting cases of this more general result. This new formula will provide a very useful tool for obtaining more reliable results for the beamwidth of any type of 1-D LWA.