Rotation Matrix ↔ Euler Angles Calculator
Convert Euler Angles (Roll, Pitch, Yaw) to a Rotation Matrix and vice versa with a live visual axis view.
📘 User Guide (Click to Open)
What Is a Rotation Matrix?
A rotation matrix is a 3×3 matrix that describes orientation in 3D space. Each value has a label:
| r11 r12 r13 | | r21 r22 r23 | | r31 r32 r33 |
What Are Euler Angles?
- Roll (X) – rotation around X-axis
- Pitch (Y) – rotation around Y-axis
- Yaw (Z) – rotation around Z-axis
Rotation Order Used
This calculator uses the industry-standard ZYX order: Yaw → Pitch → Roll.
Gimbal Lock
When pitch reaches ±90°, roll and yaw become coupled. This calculator automatically detects and handles it.
Who Should Use This?
- Robotics & Engineering students
- Game developers
- Aerospace & mechanical fields
- IMU / sensor data processing