3D Rotation Converter

Input

Input angle format Radians Degrees

Rotation matrix
 
 

Quaternion
x y z w (real part)

Axis-angle
Axis x y z Angle (radians)

Axis with angle magnitude (radians)
Axis x y z

Euler angles of multiple axis rotations (radians)
XYZ XZY YXZ YZX ZXY ZYX 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

Output angle format Radians Degrees

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) XYZ XZY YXZ YZX ZXY ZYX

Details

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.

Software

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.