Enter Vector Data
Use up to three vectors. Angles are measured from the positive x-axis. Counterclockwise angles are positive. Negative angles rotate clockwise.
Example Data Table
This worked example shows how three vectors combine into a resultant after resolving each one into rectangular components.
| Vector | Magnitude | Angle (°) | X Component | Y Component |
|---|---|---|---|---|
| Vector 1 | 10.00 | 30.00 | 8.66 | 5.00 |
| Vector 2 | 8.00 | 120.00 | -4.00 | 6.93 |
| Vector 3 | 6.00 | -45.00 | 4.24 | -4.24 |
| Resultant | 11.76 | 40.83 | 8.90 | 7.69 |
Formula Used
Horizontal component: Vx = V × cos(θ)
Vertical component: Vy = V × sin(θ)
Total horizontal component: ΣVx = Vx₁ + Vx₂ + Vx₃
Total vertical component: ΣVy = Vy₁ + Vy₂ + Vy₃
Resultant magnitude: R = √((ΣVx)² + (ΣVy)²)
Resultant angle: θr = atan2(ΣVy, ΣVx)
The calculator first resolves each vector into x and y parts, then adds those components. Finally, it computes the overall resultant magnitude and direction from the summed components.
How to Use This Calculator
- Enter the magnitude and direction for each vector.
- Select whether the entered angles are in degrees or radians.
- Choose the number of decimal places for displayed values.
- Click Resolve Vectors to calculate components and resultant values.
- Review the component table, summary cards, and graph.
- Download the final data as CSV or PDF whenever needed.
Frequently Asked Questions
1) What is vector resolution?
Vector resolution is the process of splitting one vector into perpendicular components, usually along the x-axis and y-axis. These components make addition, subtraction, and direction analysis much easier.
2) Why are x and y components useful?
They convert angled vectors into simple horizontal and vertical values. Once resolved, you can add components directly to find totals, resultants, and final directions with fewer mistakes.
3) Which angle convention does this calculator use?
It uses angles measured from the positive x-axis. Positive values rotate counterclockwise, while negative values rotate clockwise. This is a standard mathematical convention for vector analysis.
4) Can I enter radians instead of degrees?
Yes. Choose radians in the angle unit field before submitting the form. The calculator will still report the final angle in both radians and degrees for easier interpretation.
5) Why do some components become negative?
A negative component means the vector points left or downward relative to the chosen axis system. The sign simply reflects direction, not an error in the calculation.
6) What happens when I use multiple vectors?
Each vector is resolved separately. The calculator then adds all horizontal parts and all vertical parts to produce one resultant vector for the entire set.
7) Does the graph show the resultant vector?
Yes. The Plotly graph displays each entered vector from the origin and also shows the resultant vector based on the total x and y components.
8) Can I export the results for reports?
Yes. After calculation, use the CSV button for spreadsheet work or the PDF button for printable summaries. Both exports use the values shown in the results table.