Quaternion Calculator
Perform various quaternion operations for 3D rotations and mathematics
Quaternion Input
Q1 Properties
Magnitude |Q1|:1.000000
Normalized:1.0000 + 0.0000i + 0.0000j + 0.0000k
Conjugate Q1*:1.0000 + 0.0000i + 0.0000j + 0.0000k
Inverse Q1^-1:1.0000 + 0.0000i + 0.0000j + 0.0000k
Operations
Q1 + Q2:2.0000 + 0.0000i + 0.0000j + 0.0000k
Q1 - Q2:0.0000 + 0.0000i + 0.0000j + 0.0000k
Q1 * Q2 (Hamilton):1.0000 + 0.0000i + 0.0000j + 0.0000k
Dot Product:1.000000
Quaternion Formulas
- Quaternion: q = w + xi + yj + zk
- Magnitude: |q| = sqrt(w^2 + x^2 + y^2 + z^2)
- Conjugate: q* = w - xi - yj - zk
- Inverse: q^-1 = q* / |q|^2
- Hamilton Product: q1*q2 uses the rule i^2 = j^2 = k^2 = ijk = -1