Add, subtract, multiply, or normalize quaternions with a layout that keeps the live result visible beside the inputs.
Last updated: June 2026 | By Patchworkr Team
A quaternion is a four-part number written as w + xi + yj + zk. Quaternions are used in 3D rotation, computer graphics, robotics, and other applications that need stable orientation math.
This calculator supports the common component-wise operations as well as normalization, which scales a quaternion to unit length.
If Quaternion 1 is 1 + 2i + 3j + 4k and Quaternion 2 is 0 + 1i + 0j + 0k, then addition gives 1 + 3i + 3j + 4k.
No. The order of multiplication matters.
It scales the quaternion so its magnitude becomes 1.
Yes. Any finite real value is accepted in each component.
Yes. Decimal values are allowed for all quaternion components.
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