Quaternion Calculator

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The scalar (real) component of the first quaternion.
Coefficient of the i imaginary unit in q1.
Coefficient of the j imaginary unit in q1.
Coefficient of the k imaginary unit in q1.
The scalar (real) component of the second quaternion.
Coefficient of the i imaginary unit in q2.
Coefficient of the j imaginary unit in q2.
Coefficient of the k imaginary unit in q2.
X component of the rotation axis vector (does not need to be a unit vector).
Y component of the rotation axis vector.
Z component of the rotation axis vector.
The angle of rotation in degrees.
deg
Result
-60 + 12i + 30j + 24k

The full quaternion result of the selected operation.

Result real part (a)-60
Result i coefficient (b)12
Result j coefficient (c)30
Result k coefficient (d)24
Norm of result72.249567
Norm of q15.477226
Norm of q213.190906
Real (a)-60
i (b)12
j (c)30
k (d)24

Hamilton product of q1 and q2 computed.

  • Quaternion multiplication is NOT commutative: q1 * q2 generally differs from q2 * q1.
  • The norm of a product equals the product of the norms: ||q1*q2|| = ||q1|| * ||q2||.
  • The norm of the result is 72.249567.
  • Norm of the result: 72.249567.

Next stepUse the rotation mode to build a unit rotation quaternion, then conjugate it to reverse the rotation.

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