Degrees of freedom

Degrees of freedom (DOF, also written DoF) are the independent ways a rigid object can move within a space. There are a total of 6 degrees of freedom in a 3 dimensional space. The 6 DOF can be divided into 2 categories, rotational movements and translational movements, with 3 DOF in each category.

In virtual reality (VR) and augmented reality (AR), the term is most often used to distinguish two levels of head-mounted display (HMD) and motion controller tracking. A 3DoF device tracks rotational movement only (pitch, yaw, and roll), so the user can look around but the system does not register changes in physical position. A 6DoF device adds the 3 translational movements (forward/backward, left/right, up/down), so the system registers both where the user is looking and where the user has moved. The Oculus Rift CV1 and later headsets use the Constellation system for full 6 degree of freedom rotational and positional tracking. SteamVR HMDs also provide 6 DOF. Both orientation tracking (rotation) and positional tracking (translation) are tracked to register a user's full movement in VR.

Rotational movements

The 3 rotational movements are pitch, yaw, and roll. Pitch is tilting the head up or down, yaw is turning the head left or right, and roll is the ear-to-shoulder pivot. These movements are tracked by most HMDs' on-board sensors. As the user tilts and turns the head, the HMD senses the movements and alters its display accordingly.

Rotational movements are tracked by IMUs (inertial measurement units), which consist of an accelerometer, gyroscope, and optionally a magnetometer. These IMUs measure the HMD's acceleration, angular velocity, and (with a magnetometer) the surrounding magnetic field to infer rotational orientation and movement. An IMU that has a magnetometer is often marketed as having "9 DOF". In this usage "9 DOF" counts the nine sensor axes (3 from the accelerometer, 3 from the gyroscope, and 3 from the magnetometer) rather than nine independent ways an object can move; a rigid body still has only the 6 spatial degrees of freedom described above, and the magnetometer's 3 axes add a directional (magnetic heading) reference used in sensor fusion, not 3 extra real degrees of freedom.

Translational movements

The 3 translational movements are left/right, forward/backward and up/down. Three dimensions are also referred to as X,Y,Z, but some people and programs use XYZ to mean lateral, vertical, depth, in that order, whereas others use it to mean lateral, depth, vertical, or others. Translational movements were historically tracked by an external camera or other sensors; modern standalone headsets track them with on-board cameras using markerless inside-out tracking.

The ability to track translational movements is required for positional tracking (positional tracking is the ability to determine the absolute position of an object in a 3D environment).

3DoF and 6DoF headsets

3DoF headsets are typically lower cost devices, including smartphone holders and early standalone units, that detect head orientation only. 6DoF headsets add full positional tracking and allow the user to move through the virtual space. The table below lists representative examples.

Examples of 3DoF and 6DoF headsets

Degrees of freedom	Example headsets
3DoF (rotational only)	Google Cardboard, Samsung Gear VR, Oculus Go, Google Daydream View
6DoF (rotational and translational)	Oculus Rift CV1 and later, Meta Quest series (Oculus Quest, Quest 2, Quest 3), HTC Vive, Valve Index, PlayStation VR2, Apple Vision Pro

3DoF and 6DoF controllers

The same distinction applies to motion controllers, and a headset's degrees of freedom do not always match its controllers'. A 3DoF controller, such as the Samsung Gear VR Controller, the Google Daydream controller, or the controller bundled with the Oculus Go, reports orientation only: it can point and tilt but its position in the room is not tracked. A 6DoF controller, such as the Oculus Touch controllers on the Meta Quest series or the Sense controllers on the PlayStation VR2, is tracked in both rotation and position, so its movement maps to a virtual hand. Google described these combinations with a two-number notation: a "3.3" device pairs a 3DoF headset with 3DoF controllers, while a "6.3" device pairs a 6DoF headset with 3DoF controllers, as on the standalone Daydream platform.