1. The kinematics of the human angular vestibuloocular reflex (VOR) in three dimensions was investigated in 12 normal subjects during high-acceleration head rotations (head “impulses”). A head impulse is a passive, unpredictable, high-acceleration (3,000–4,000 degrees/s2) head rotation of approximately 10–20 degrees in roll, pitch, or yaw, delivered with the subject in the upright position and focusing on a fixation target. Head and eye rotations were measured with dual search coils and expressed as rotation vectors. The first of these two papers describes a vector analysis of the three-dimensional input-output kinematics of the VOR as two indexes in the time domain: magnitude and direction. 2. Magnitude is expressed as speed gain (G) and direction as misalignment angle (delta). G is defined as the ratio of eye velocity magnitude (eye speed) to head velocity magnitude (head speed). delta is defined as the instantaneous angle by which the eye rotation axis deviates from perfect alignment with the head rotation axis in three dimensions. When the eye rotation axis aligns perfectly with the head rotation axis and when eye velocity is in a direction opposite to head velocity, delta = 0. The orientation of misalignment between the head and the eye rotation axes is characterized by two spatial misalignment angles, which are the projections of delta onto two orthogonal coordinate planes that intersect at the head rotation axis. 3. Time series of G were calculated for head impulses in roll, pitch, and yaw. At 80 ms after the onset of an impulse (i.e., near peak head velocity), values of G were 0.72 +/- 0.07 (counterclockwise) and 0.75 +/- 0.07 (clockwise) for roll impulses, 0.97 +/- 0.05 (up) and 1.10 +/- 0.09 (down) for pitch impulses, and 0.95 +/- 0.06 (right) and 1.01 +/- 0.07 (left) for yaw impulses (mean +/- 95% confidence intervals). 4. The eye rotation axis was well aligned with head rotation axis during roll, pitch, and yaw impulses: delta remained almost constant at approximately 5–10 degrees, so that the spatial misalignment angles were < or = 5 degrees. delta was 9.6 +/- 3.1 (counterclockwise) and 9.0 +/- 2.6 (clockwise) for roll impulses, 5.7 +/- 1.6 (up) and 6.1 +/- 1.9 (down) for pitch impulses, and 6.2 +/- 2.2 (right) and 7.9 +/- 1.5 (left) for yaw impulses (mean +/- 95% confidence intervals). 5. VOR gain (gamma) is the product of G and cos(delta). Because delta is small in normal subjects, gamma is not significantly different from G. At 80 ms after the onset of an impulse, gamma was 0.70 +/- 0.08 (counterclockwise) and 0.74 +/- 0.07 (clockwise) for roll impulses, 0.97 +/- 0.05 (up) and 1.09 +/- 0.09 (down) for pitch impulses, and 0.94 +/- 0.06 (right) and 1.00 +/- 0.07 (left) for yaw impulses (mean +/- 95% confidence intervals). 6. VOR latencies, estimated with a latency shift method, were 10.3 +/- 1.9 (SD) ms for roll impulses, 7.6 +/- 2.8 (SD) ms for pitch impulses, and 7.5 +/- 2.9 (SD) ms for yaw impulses. 7. We conclude that the normal VOR produces eye rotations that are almost perfectly compensatory in direction as well as in speed, but only during yaw and pitch impulses. During roll impulses, eye rotations are well aligned in direction, but are approximately 30% slower in speed.