Current clinical ultrasound (US) systems are limited to show blood flow movement in either 1-D or 2-D. In this paper, a method for estimating 3-D vector velocities in a plane using the transverse oscillation method, a 32×32 element matrix array, and the experimental US scanner SARUS is presented. The aim of this paper is to estimate precise flow rates and peak velocities derived from 3-D vector flow estimates. The emission sequence provides 3-D vector flow estimates at up to 1.145 frames/s in a plane, and was used to estimate 3-D vector flow in a cross-sectional image plane. The method is validated in two phantom studies, where flow rates are measured in a flow-rig, providing a constant parabolic flow, and in a straight-vessel phantom ( ∅=8 mm) connected to a flow pump capable of generating time varying waveforms. Flow rates are estimated to be 82.1 ± 2.8 L/min in the flow-rig compared with the expected 79.8 L/min, and to 2.68 ± 0.04 mL/stroke in the pulsating environment compared with the expected 2.57 ± 0.08 mL/stroke. Flow rates estimated in the common carotid artery of a healthy volunteer are compared with magnetic resonance imaging (MRI) measured flow rates using a 1-D through-plane velocity sequence. Mean flow rates were 333 ± 31 mL/min for the presented method and 346 ± 2 mL/min for the MRI measurements.