This research extends the theory of binomial array antennas. A closed-form expression for the half-power beamwidth of the array factor of an array antenna is presented. The expression is correct for the ratios of element spacing to wavelength greater than or equal to one quarter. Also, exact equations for determining the half-power beamwidth for main-beam steering are derived. A comparison with an approximate formula for the half-power beamwidth of binomial array antennas is carried out.