Examples
Examples
Try the starting example
- Vector to rotate, x,y,z
- 1,0,0
- Rotation input: axis-angle or quaternion
- axis-angle
- Axis x,y,z
- 0,0,1
- Right-handed angle (degrees)
- 90
- Quaternion w,x,y,z
- 1,0,0,0
- Rotated vector
- 0, 1, 0
- Normalised quaternion w,x,y,z
- 0.707106781187, 0, 0, 0.707106781187
- Original vector norm
- 1
- Rotated vector norm
- 1
Try another scenario
- Vector to rotate, x,y,z
- 1,0,0
- Rotation input: axis-angle or quaternion
- quaternion
- Axis x,y,z
- 0,0,1
- Right-handed angle (degrees)
- 90
- Quaternion w,x,y,z
- 0,0,0,2
- Rotated vector
- -1, 0, 0
- Normalised quaternion w,x,y,z
- 0, 0, 0, 1
- Original vector norm
- 1
- Rotated vector norm
- 1
Calculation method
Calculation method
Rotated vector
Apply the unit-quaternion rotation q×(0,v)×conjugate(q), using the equivalent dot/cross-vector expression.
Normalised quaternion w,x,y,z
For axis-angle, normalise the axis and use (cos(angle/2),axis×sin(angle/2)); otherwise normalise the four supplied quaternion components.
Original vector norm
Euclidean norm before rotation.
Rotated vector norm
Euclidean norm after rotation; rigid rotation should preserve this up to roundoff.
Symbols and units
- a
- Vector to rotate, x,y,z
- b
- Rotation input: axis-angle or quaternion
- c
- Axis x,y,z
- d
- Right-handed angle (degrees)
- e
- Quaternion w,x,y,z
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Right-handed active rotation in three-dimensional Euclidean coordinates, with quaternion order w,x,y,z. Zero axes or zero quaternions in the selected input mode are rejected. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
ROS 2: quaternion fundamentals and rotation conventions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.