2D VECTOR ADDITION CALCULATOR

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.

Addition of 2D Vectors

2D Vector Addition Formulas

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:

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

 

Additional Resources