| Label | Input mode | Magnitude | Angle (°) | X | Y | Color | Actions |
|---|
Results
| ΣX | 0 |
|---|---|
| ΣY | 0 |
| Resultant magnitude |R| | 0 |
| Resultant angle θ (°) | 0 |
Angles measured from +x axis, counterclockwise. Input angles use selected unit.
Example Data
| Label | Mode | Magnitude | Angle | X | Y | Color |
|---|---|---|---|---|---|---|
| A | Mag+Angle | 5 | 30° | 4.3301 | 2.5 | Blue |
| B | Mag+Angle | 4 | 120° | -2 | 3.4641 | Green |
| C | Components | — | — | 1 | -3 | Red |
Formula Used
For each vector \(i\):
Given magnitude \(m_i\) and angle \(\theta_i\):
\(x_i = m_i\cos\theta_i,\quad y_i = m_i\sin\theta_i\)
Given components \(x_i, y_i\):
\(m_i = \sqrt{x_i^2 + y_i^2},\quad \theta_i = \operatorname{atan2}(y_i, x_i)\)
Summation and resultant:
\(\Sigma X = \sum_i x_i,\quad \Sigma Y = \sum_i y_i\)
\(|R| = \sqrt{(\Sigma X)^2 + (\Sigma Y)^2}\)
\(\theta_R = \operatorname{atan2}(\Sigma Y, \Sigma X)\)
How to Use
- Choose an input mode per row: components or magnitude+angle.
- Select your preferred angle unit from the toolbar.
- Pick a color preset for each vector row.
- Press Compute to update results and graph.
- Toggle head‑to‑tail or origin mode, grid, and labels as needed.
- Use Download CSV or Download PDF for exports.
FAQs
Angles are measured in degrees from the positive x‑axis, counterclockwise. Switch the unit selector to radians if needed; calculations adapt instantly and displays update consistently.
Yes. Choose “Radians” in the angle unit selector. Angle inputs, conversions, and the resultant angle will all use radians for display and editing.
No. Color presets only affect the visualization. They help distinguish vectors and improve readability in the graph and exported PDF.
Displayed values are rounded to four decimals for readability. Internal calculations use JavaScript floating‑point precision, suitable for most engineering and classroom uses.
Head‑to‑tail draws each vector starting from the previous head. Origin mode draws all vectors from the origin to compare directions side‑by‑side.
Yes. CSV includes each vector’s color and the current angle unit. The resultant row stores the resultant magnitude plus angle in the chosen unit.