Vector Magnitude Calculator

Your details

Choose how many components your vector has.
Reveals the normalised unit vector and the direction angles (degrees) for 3D vectors.
Magnitude |v|Non-zero vector
5
|v|² (sum of squares)25
Unit vector x-hat0.6
Unit vector y-hat0.8
Unit vector z-hat0
Direction angle alpha (x-axis)53.1301deg
Direction angle beta (y-axis)36.8699deg
Direction angle gamma (z-axis)90deg
Direction cosine cos(alpha)0.6
Direction cosine cos(beta)0.8
Direction cosine cos(gamma)0
x-hat0.6
y-hat0.8
z-hat0

The magnitude of this 3D vector is 5.

  • This 3D vector has magnitude 5, the straight-line distance from the origin to its tip.
  • Magnitude is always zero or positive because it captures size, not direction. Reversing every component sign leaves it unchanged.
  • The unit vector is (0.6, 0.8, 0), pointing the same way with length 1.
  • The direction angles are alpha = 53.13 deg (from x-axis), beta = 36.87 deg (from y-axis), gamma = 90 deg (from z-axis).

Next stepUse the unit vector components above to describe the direction without a length, or multiply them by any scalar to scale the vector.

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