Quaternion Magnitude Calculator
Online calculator to calculate the length of a quaternion
The function on this page calculates the magnitude (length) of a quaternion. The length or the square of the length can be calculated.
To perform the calculation, select the mathematical function to be calculated and enter the values of the quaternion. Then click on the 'Calculate' button.
Empty fields count as 0.
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Description
The quaternion represents a vector used to encode three-dimensional physical rotations. It is used to efficiently rotate an object around the (x,y,z) vector by angle theta, where the following applies:
w = cos(theta/2)
Components
W - The rotation component.
X - The X value of the vector component.
Y - The Y value of the vector component.
Z - The Z value of the vector component.
Functions
Magnitude (length)
The magnitude (or length) of a quaternion corresponds to the magnitude of a four-dimensional vector. Therefore the formula applies:
\(||q||=||w+ ix+iy+iz||=\sqrt{w^2+x^2+y^2+z^2} \)
Square of length
Calculates the square of the magnitude or length of the quaternion.
\(||q||=||w+ ix+iy+iz||=w^2+x^2+y^2+z^2\)
More Quaternion Functions
Addition • Subtraction • Division • Multiplication • Concatenate • Length • Interpolation • Normalize • Scalar Multiplication • Dot Product • Yaw-Pitch-Roll
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