Direction of the Vector Calculator

Your details

Choose whether your vector has two or three components.
The horizontal component of the vector.
The vertical component of the vector.
Display the direction angle in degrees (0 to 360) or radians (0 to 2pi).
Direction angle
53.1301

Angle from the positive x-axis, measured counter-clockwise (degrees or radians).

Magnitude5
QuadrantQuadrant I
Unit vector x0.6
Unit vector y0.8
cos α (x-axis)0.6
cos β (y-axis)0.8
Angle with x-axis53.13
Angle with y-axis36.87
Unit x0.6
Unit y0.8
Unit z-

Direction angle: 53.13 degrees. Magnitude: 5.0000.

  • The vector lies in Quadrant I, so the direction angle is 53.13 degrees from the positive x-axis.
  • The magnitude (length) of this vector is 5.0000, and the unit vector has magnitude exactly 1.
  • Direction cosines cos(alpha) = 0.6000 and cos(beta) = 0.8000 equal the unit vector components.
  • The sum of squares of all direction cosines always equals 1, confirming the unit vector is correct.

Next stepPair the direction angle with the magnitude to fully describe the vector in polar form.

 = Powered by OnlyCalculators