Enter Vector Data
Use polar inputs or direct components. The calculator keeps a single-column page layout, while the input fields adapt to large, medium, and small screens.
Formula Used
For polar inputs: xi = mi cos(θi) and yi = mi sin(θi).
Total components: Rx = Σxi and Ry = Σyi.
Resultant magnitude: |R| = √(Rx2 + Ry2).
Direction: θ = atan2(Ry, Rx).
How to Use This Calculator
- Select how many vectors you want to combine.
- Choose polar mode for magnitude and angle, or component mode for X and Y entries.
- Set your preferred angle unit and decimal precision.
- Enter values for each active vector row.
- Press the calculate button to display the resultant above the form.
- Review components, direction, unit vector, equilibrant, table output, and plot.
- Use the CSV or PDF buttons to export your result summary.
Example Data Table
| Vector | Magnitude | Angle (°) | X Component | Y Component |
|---|---|---|---|---|
| V1 | 10.0000 | 0.0000 | 10.0000 | 0.0000 |
| V2 | 8.0000 | 60.0000 | 4.0000 | 6.9282 |
| V3 | 6.0000 | 210.0000 | -5.1962 | -3.0000 |
| Resultant | 9.6407 | 24.0418 | 8.8038 | 3.9282 |
Frequently Asked Questions
1. What is a resultant vector?
A resultant vector is the single vector that represents the combined effect of two or more vectors. It includes both total magnitude and final direction.
2. Can I enter vectors as components instead of angles?
Yes. Choose component mode and enter X and Y values for each vector. The calculator will derive magnitude and direction automatically from those components.
3. Does the calculator support degrees and radians?
Yes. You can switch between degrees and radians before calculating. Internally, the tool converts the values correctly for trigonometric operations.
4. What direction reference does the calculator use?
Angles are measured from the positive X-axis in a counterclockwise direction. This is the standard convention used in coordinate geometry and vector analysis.
5. What is the equilibrant vector?
The equilibrant has the same magnitude as the resultant but points in the opposite direction. It would exactly balance the resultant if both acted together.
6. Why is my direction shown in a different quadrant than expected?
Direction depends on the signs of the final X and Y totals. Even if individual vectors point elsewhere, their combined components determine the final quadrant.
7. What does the Plotly graph show?
The graph displays each input vector from the origin, a head-to-tail cumulative path, and the final resultant vector. This helps visualize magnitude and direction together.
8. Can I export the results?
Yes. Use the CSV button for spreadsheet-style data and the PDF button for a formatted report that includes vector entries and summary measurements.