2D vector addition calculator calculates the sum of the 2 dimensional vectors. Either the components or magnitude/direction angle values of the vectors can be entered for the calculations. Up to 5 vectors can be added at once with the calculator.

The vector $${ \vec { A } }$$ is:

$$\vec {A} ={A}_{x}\hat {x} +{A}_{y}\hat {y}$$

The magnitude of the vector $${ \vec { A } }$$ is:

$$\left| A \right| =\sqrt { { { A }_{ x } }^{ 2 }+{ { A }_{ y } }^{ 2 } }$$

The x-component of the vector $${ \vec { A } }$$ is:

$${A}_{x}=A\cos {\theta}$$

The y-component of the vector $${ \vec { A } }$$ is:

$${A}_{y}=A\sin {\theta}$$

The angle of the vector $${ \vec { A } }$$ is:

$$\tan{\theta} =\frac{{A}_{y}}{{A}_{x}}$$

The sum of vectors is:

$$\vec { R } =\vec { A } +\vec { B }….+\vec { E }$$
$${ R }_{ x }={ A }_{ x }+{ B }_{ x }….+{ E }_{ x }$$
$${ R }_{ y }={ A }_{ y }+{ B }_{ y }….+{ E }_{ y }$$