Adding Vectors Calculator


Two online calculators to add two vectors are presented. The vectors are either given by their components or theit magnitude and direction. The results of calculations are given by the components of the resultant , and also its magnitude and direction. .

Let \(\mathbf{u}\) and \(\mathbf{v}\) be two vectors given in component form by \[ \mathbf{u} = \langle u_1, u_2 \rangle \quad \text{and} \quad \mathbf{v} = \langle v_1, v_2 \rangle. \] The addition of the two vectors \(\mathbf{u}\) and \(\mathbf{v}\) is defined by \[ \mathbf{u} + \mathbf{v} = \langle u_1 + v_1, \, u_2 + v_2 \rangle. \]

Use of the Adding Vectors Calculator

There are two calculators that may be used to add two vectors depending on whether you know the components or the magnitude and directions of the vectors to add.
1 - Enter the components \( u_1, u_2 \text{ and } v_1, v_2 \) of the two vectors \(\mathbf{u}\) and \(\mathbf{v}\) respectively as real numbers and press "Add the Two Vectors". The outputs are the components of vector \( \mathbf{u} + \mathbf{v} \) , its magnitude and direction in degrees.

\( u_1 \) = , \( u_2 \) =
\( v_1 \) = , \( v_2 \) =
Decimal Places =
\( \mathbf{u} + \mathbf{v} \) = < , >
Magnitude: \( || \mathbf{u} + \mathbf{v} || \) =
Direction of \( \mathbf{u} + \mathbf{v} \) = θ = °


2 - Enter the magnitudes (non negative real) and directions,in degrees, of the two vectors \( \mathbf{u} \) and \( \mathbf{v} \) respectively as real numbers and press "Add the Two Vectors". The outputs are the components of vector \( \mathbf{u} + \mathbf{v} \) , its magnitude and direction in degrees.

\( || \mathbf{u} || \) = , Direction of \( \mathbf{u}\) =
\( || \mathbf{v} || \) = , Direction of \( \mathbf{v} \) =
Decimal Places =
\( \mathbf{u} + \mathbf{v} \) = < , >
Magnitude of \( \mathbf{u} + \mathbf{v} \) =
Direction of\( \mathbf{u} + \mathbf{v} \) = θ = °

More References and Links

Find Magnitude and Direction of Vectors. vector calculators
Vector Addition and Scalar Multiplication.