Rotation Matrix Calculator

Generate 3D rotation matrices from Euler angles, quaternions, or axis-angle

Input Type

Rotation Order

Roll (X) degrees

Pitch (Y) degrees

Yaw (Z) degrees

Rotation Matrix R

R =

1.0000000.0000000.000000

0.0000001.0000000.000000

0.0000000.0000001.000000

Determinant: 1.000000 (valid rotation matrix)

Transpose (Inverse for Rotation)

R^T =

1.0000000.0000000.000000

0.0000001.0000000.000000

0.0000000.0000001.000000

Rotation Matrix Properties

For a valid rotation matrix: det(R) = 1
R^T = R^(-1) (transpose equals inverse)
Columns and rows are orthonormal unit vectors
Preserves vector lengths and angles