Vectors are the language of physics, representing quantities with both magnitude and direction. The Vector Triangle Calculator uses the ‘Triangle Law of Vector Addition’ to combine two vectors placed head-to-tail and find the resultant vector—the direct path from the start to the finish.
Features
Component Resolution: Breaks down Vectors A and B into their X and Y components automatically.
Resultant Calculation: Finds the magnitude and angle of the final Resultant Vector (R).
Visual Addition: Displays the vectors head-to-tail on a grid to demonstrate the addition visually.
Coordinate Output: Provides both polar (magnitude/angle) and Cartesian (x,y) results.
How to Use This Calculator
Define Vector A: Enter the magnitude (length) and angle for the first vector.
Define Vector B: Enter the magnitude and angle for the second vector.
Calculate: Click to see how they combine.
Visualize: The graph shows Vector A starting at the origin, Vector B starting from A’s tip, and the Red Resultant connecting the start to the end.
Formulas
The calculator uses the following mathematical principles:
X-Component: $$ V_x = |V| \cdot \cos(\theta) $$
Y-Component: $$ V_y = |V| \cdot \sin(\theta) $$
Resultant X: $$ R_x = A_x + B_x $$
Resultant Magnitude: $$ |R| = \sqrt{R_x^2 + R_y^2} $$
Practical Applications
Physics: Calculating net force or total displacement.
Engineering: Analyzing stress vectors in structural members.
Game Development: Computing character movement when multiple forces (input + wind) apply.
Tips for Success
Angle System: This calculator uses standard mathematical angles (0° is East, 90° is North, Counter-Clockwise).
Head-to-Tail: The visualization places the tail of Vector B at the head of Vector A, which is the standard way to visualize addition.
Negative Components: Don’t worry about quadrants; the calculator handles negative x/y values automatically.
Frequently Asked Questions (FAQ)
Can I subtract vectors?
Yes, you can add a vector with the same magnitude but an angle 180° opposite.
What is the Resultant?
The resultant is the single vector that has the same effect as the combined original vectors.
Final Words
Combine forces with confidence. The Vector Triangle Calculator simplifies complex vector addition into clear, visual steps, making physics problems and motion analysis straightforward.
