This calculator allows you to convert between rotations in 3D space described in axis-angle format, quaternions, rotation matrices and Euler angles (with an abitrary axis order). It also shows you how the rotation would rotate reference frame one to reference frame two in the below graph.

The radio button determines what rotation form is user input, the others are calculated from this (outputs).

\(\theta\) | |

\(x\) | |

\(y\) | |

\(z\) |

\(w\) | |

\(x\) | |

\(y\) | |

\(z\) |

X | |

Y | |

Z |

Currently this calculator only supports intrinsic Euler angles (extrinsic Euler angles are not supported). The choice of rotation unit (radians or degrees) effects the interpretation of the theta in angle-axis form and all three Euler angles.

Care must be taken when inputting either quaternions or rotation matrices, as not all quaternions or rotation matrices produce valid rotations. The norm of the quaternion must equal 1. The rotation matrix must be an orthogonal matrix.