Angle Between Two Vectors Calculator

Your details

Choose 2D for planar vectors or 3D for vectors in space.
The x-component of vector A.
The y-component of vector A.
The z-component of vector A.
The x-component of vector B.
The y-component of vector B.
The z-component of vector B.
AngleAcute angle
12.9332degrees

Angle between the two vectors in degrees (0 to 180)

Angle (radians)0.225726rad
Dot product32
|A| magnitude3.7417
|B| magnitude8.775
12.9332 deg
Parallel<0.001Acute0.001-90Right90-90.001Obtuse90.001+

The angle is 12.9332 degrees (0.225726 rad).

  • The vectors form an acute angle of 12.9332 degrees. A positive dot product (32.0000) confirms they lean toward each other.
  • The magnitudes are |A| = 3.7417 and |B| = 8.7750.
  • The angle between two vectors is always between 0 and 180 degrees (0 and pi radians).

Next stepTo find the projection of A onto B, multiply |A| by cos(theta). Projections are central to regression, signal processing and computer graphics.

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