Magnitude and Direction of a Vector - Calculator

An online calculator to calculate the magnitude and direction of a vector from it components.

Let v be a vector given in component form by
v = < v1 , v2 >
The magnitude || v || of vector v is given by
|| v || = √(v1 2 + v2 2)
and the direction of vector v is angle θ in standard position such that
tan(θ) = v2 / v1 such that 0 ≤ θ < 2π.


Use of the calculator to Calculate Magnitude and Direction

1 - Enter the components v1 and v2 of vector v as real numbers and press "Calculate Magnitude and Direction". The outputs are the magnitude || v || and direction θ in degrees of vector v.

v1 = , v2 =
Decimal Places =
Magnitude: ||v|| =
Direction: θ =


Use the calculator of Magnitude and Direction to Answer the Questions

  1. Use the calculator to find the direction of the vectors u = < - 2 , 3 > and v = < - 4 , 6 >. Why are they equal?
  2. Find the direction of the vectors u = < 2 , 5 > and v = < - 2 , - 5 >. Why is the difference between the two directions equal to 180?
  3. Use the calculator to find the direction of the vectors u = < 2 , 1 > and v = < 1 , 2 >. Why is the sum of the two directions equal to 90? Find other pairs of vectors whose directions add up to 90

More References and Links

Find magnitude and direction of vectors
Vector Calculators.
Vector Addition and Scalar Multiplication.