Quaternion Rotation Calculator
Rotate 3D points using quaternion rotation (p' = q * p * q^-1)
Rotation Input Mode
Point to Rotate
Results
Normalized Quaternion:
(1.0000, 0.0000, 0.0000, 0.0000)
Rotated Point:
(1.0000, 0.0000, 0.0000)
Rotation Angle
0.00°
Rotation Axis
(0.000, 0.000, 1.000)
Quaternion Rotation Formula
To rotate a point p by quaternion q:
p' = q * p * q^(-1)
Where p is represented as a pure quaternion (0, px, py, pz)
From axis-angle (axis u, angle theta):
q = (cos(theta/2), u * sin(theta/2))