2D Vector Addition Calculator & Visualizer
In kinematics and dynamics, forces and velocities are vectors: quantities with both magnitude and direction. Solving multi-vector problems graphically or analytically can be tedious. This interactive Vector Addition Calculator immediately resolves multiple 2D vectors into a single resultant vector.
Input up to 5 vectors using either Cartesian components (x, y) or polar coordinates (magnitude |R|, angle θ). The canvas dynamically plots each vector head-to-tail alongside the bold resultant vector, making the underlying trigonometric decompositions entirely transparent.
Vectors
Analytical Vector Addition
To add vectors analytically, you must break them down into orthogonal components (usually x and y axes). The fundamental equations for vector decomposition are:
- \( V_x = |V| \times \cos(\theta) \)
- \( V_y = |V| \times \sin(\theta) \)
Once all vectors are decomposed into Cartesian form, simply sum all the x-components and y-components together to find the Resultant Vector (R). Finally, to find the magnitude and direction of the resultant, use the Pythagorean theorem and inverse tangent:
- Magnitude: \( |R| = \sqrt{R_x^2 + R_y^2} \)
- Direction: \( \theta = \tan^{-1}(R_y / R_x) \)