Rotation Matrix

2D and 3D rotation matrices from angles

R(θ) = [[cos θ, −sin θ], [sin θ, cos θ]]
Rotation matrix R
0,866-0,5
0,50,866
Determinant det(R)
1

A proper rotation preserves length and orientation, so det(R) = 1.

Each column of R is where a standard basis vector lands after the rotation.

Rotation MatrixA 2D plane with the standard axes rotated by 30°. The arrows e₁ and e₂ are the rotated unit vectors î and ĵ, which form the columns of the rotation matrix.e₁e₂θ = 30°

Sobre esta calculadora

The Rotation Matrix Calculator builds the 2D rotation matrix R(θ) = [[cosθ, −sinθ], [sinθ, cosθ]] from a single angle, or the 3D matrix R = Rz·Ry·Rx (yaw–pitch–roll, ZYX order) from three angles. It works in degrees or radians, gives exact entries at special angles, confirms that det(R) = 1, and draws the rotated basis vectors so you can see what the matrix does. Useful for linear algebra, computer graphics, robotics, and physics.