The orientation dependence of the primary dendrite spacing is examined through the solidification of a succinonitrile-3.61 wt pct acetone alloy with a Bridgman-type device. Primary dendrite spacing has been studied as a function of the primary dendrite trunk orientation with respect to the thermal gradient direction under different growth rate conditions. The observations show that the orientation dependence of the primary dendrite spacing can be related to the formation of new primary dendrites at divergent grain boundariesvia the branching mechanism. A branching-based model is developed to study the interaction between secondary and tertiary dendrite arms. Based on this model, a simple analytical relationship is proposed to account for the orientation dependence of the primary dendrite spacing.