Quaternion ↔ Euler angle converter
Get your frames straight. Convert roll, pitch and yaw in degrees to ROS-order quaternions, or normalize a quaternion and convert back. Explicit axis conventions and gimbal-lock handling.
YOUR RESULT
- x
- 0
- y
- 0
- z
- 0.707107
- w
- 0.707107
Calculations run in your browser. No account or upload required.
How to use this calculator
- Choose Euler → quaternion or quaternion → Euler.
- Enter angles in degrees or all four quaternion components.
- Copy the result with its convention. Non-unit quaternions are normalized.
Formula & convention
R = Rz(yaw) · Ry(pitch) · Rx(roll). Quaternion component order: x, y, z, w.
Worked example
Roll 0°, pitch 0°, yaw 90° gives x=0, y=0, z≈0.707107, w≈0.707107.
Assumptions & limits
Uses active, right-handed rotations with fixed-axis roll X, pitch Y, yaw Z (equivalent to intrinsic ZYX). Euler angles are not unique. At pitch ±90° we choose roll=0 and report gimbal lock. Confirm your library’s convention; some use w,x,y,z.