Medical ultrasound (US) is a commonly used modality for image-guided procedures. Recent research systems providing an in situ visualization of 2D US images via an augmented reality (AR) head-mounted display (HMD) were shown to be advantageous over conventional imaging through reduced task completion times and improved accuracy. In this work, we continue in the direction of recent developments by describing the first AR HMD application visualizing real-time volumetric (3D) US in situ for guiding vascular punctures. We evaluated the application on a technical level as well as in a mixed-methods user study with a qualitative prestudy and a quantitative main study, simulating a vascular puncture. Participants completed the puncture task significantly faster when using 3D US AR mode compared to 2D US AR, with a decrease of 28.4% in time. However, no significant differences were observed regarding the success rate of vascular puncture (2D US AR-50% vs. 3D US AR-72%). On the technical side, the system offers a low latency of 49.90 ± 12.92 ms and a satisfactory frame rate of 60 Hz. Our work shows the feasibility of a system that visualizes real-time 3D US data via an AR HMD, and our experiments show, furthermore, that this may offer additional benefits in US-guided tasks (i.e., reduced task completion time) over 2D US images viewed in AR by offering a vividly volumetric visualization.