Unit Vector Calculator

Your details

Choose whether your vector lives in a 2D plane or 3D space.
The horizontal (x-axis) component of your vector.
The vertical (y-axis) component of your vector.
The depth (z-axis) component. Only used in 3D mode.
Unit for the direction angles displayed in the results.
Unit vector xNormalized successfully
0.6

x-component of the normalized vector

Magnitude |v|5
Unit vector y-0.8
Unit vector z0
Angle with x-axis (alpha)53.1301
Angle with y-axis (beta)143.1301
Angle with z-axis (gamma)90
Verify: unit vector magnitude1
x0.6
y-0.8
z0

Unit vector found - magnitude of result is exactly 1.

  • The original vector has magnitude 5.0000, which is how much each component is scaled down to produce the unit vector.
  • Each component is divided by 5.0000: the unit vector is (0.6000, -0.8000, 0.0000).
  • The angle between this unit vector and the positive x-axis is 53.1301 deg (53.13 deg).
  • In 3D, direction cosines alpha, beta, and gamma satisfy cos²(alpha) + cos²(beta) + cos²(gamma) = 1, which you can verify from the components above.

Next stepUnit vectors are used in dot products to find angles between vectors, in cross products to find perpendicular directions, and as basis vectors in coordinate systems.

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