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Matrix Properties
- Determinant:
Transpose (Inverse Matrix R⁻¹)
Result: R · v = v'
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Master 2D Rotations in Seconds
This tool simplifies complex transformations into two easy steps. Get the exact matrix you need for your project without manual calculations.
- Set the Angle: Use the interactive slider or type a precise degree value to define your rotation.
- Enter Your Vector: Input the X and Y coordinates of the vector you wish to transform.
- Instantly View Results: The matrix, its properties, and the transformed vector update in real-time as you make changes.
An Interactive Workspace
Go beyond simple answers. This calculator is a complete workspace for understanding and using 2D rotation matrices.
- Live Vector Transformation: See how the matrix affects a vector instantly—the most practical application of this math.
- Instant Matrix Properties: Check the Determinant to verify a proper rotation (it should be 1) and view the Transpose, which is also the inverse for rotation matrices.
- Copy to Clipboard: A single click copies the formatted 2x2 matrix, ready to be pasted into your code in any game engine or graphics library.
Why 2D Rotation Matters
The 2D rotation matrix is a fundamental building block in countless fields, translating a simple angle into powerful computational action.
- Game Development: Essential for rotating player sprites, enemies, UI elements, and aiming projectiles.
- Computer Graphics: Used in everything from photo collage maker tools and photo editing software to UI/UX design for rotating icons and creating loading animations.
- Robotics & Simulation: Forms the basis for orienting simple robotic arms and simulating the movement of 2D objects.
- Mathematical Education: Provides a clear, visual way to understand the relationship between trigonometry (
cos,sin) and linear algebra.
