3D Rotation Converter


Input angle format

Rotation matrix

x y z w (real part)

Axis x y z Angle (radians)

Axis with angle magnitude (radians)
Axis x y z

Euler angles of multiple axis rotations (radians)
x y z

Triple of points, P, Q, R, such that X ∥ (Q−P),   Z ∥ X × (R−P),  and Y ∥ Z × X.
P: x y z
Q: x y z
R: x y z


Output angle format

Rotation matrix

Quaternion [x, y, z, w]

Axis-Angle {[x, y, z], angle (radians)}

Axis with angle magnitude (radians) [x, y, z]

Euler angles (radians)


Please note that rotation formats vary. For quaternions, it is not uncommon to denote the real part first. Euler angles can be defined with many different combinations (see definition of Cardan angles). All input is normalized to unit quaternions and may therefore mapped to different ranges. The converter can therefore also be used to normalize a rotation matrix or a quaternion. Results are rounded to seven digits.


This calculator for 3D rotations is open-source software. If there are any bugs, please push fixes to the Rotation Converter git repo. For almost all conversions, three.js Math is used internally.