Calculator Form
Use standard physics convention here: 0° points along the positive X-axis, and positive rotation is counterclockwise.
Example Data Table
This worked example uses three velocity vectors in magnitude-angle form and shows the resulting combined motion.
| Vector | Magnitude (m/s) | Angle (deg) | X Component (m/s) | Y Component (m/s) |
|---|---|---|---|---|
| V1 | 12.0000 | 25.0000 | 10.8757 | 5.0714 |
| V2 | 8.0000 | 120.0000 | -4.0000 | 6.9282 |
| V3 | 5.0000 | -40.0000 | 3.8302 | -3.2139 |
| Resultant | 13.8494 | 39.3736 | 10.7059 | 8.7857 |
Formula Used
Component conversion
Vx = V × cos(θ)
Vy = V × sin(θ)
Resultant components
Rx = ΣVx
Ry = ΣVy
Resultant magnitude and heading
|R| = √(Rx2 + Ry2)
θR = atan2(Ry, Rx)
When component mode is selected, the calculator skips the first conversion step because the velocity components are entered directly.
How to Use This Calculator
- Select how many velocity vectors you want to combine.
- Choose either magnitude-angle input or direct X-Y component input.
- Set the angle unit, decimal precision, and preferred velocity unit label.
- Enter each vector carefully. Use negative component values or negative angles when needed.
- Click the calculate button to display the resultant above the form.
- Review the magnitude, heading, component table, and Plotly graph.
- Use the CSV or PDF buttons to export the result summary.
FAQs
1. What does a resultant velocity vector represent?
It represents the single velocity vector that has the same overall effect as all entered vectors combined. Its magnitude shows net speed, and its angle shows final motion direction.
2. Can I enter more than two vectors?
Yes. This calculator supports two through six vectors in one calculation, which helps with complex motion, relative velocity problems, and multi-stage movement analysis.
3. What angle convention does this page use?
It uses the standard mathematical convention. Zero starts on the positive X-axis, and positive angles rotate counterclockwise unless you enter negative values.
4. When should I use component mode?
Use component mode when your physics problem already gives horizontal and vertical velocity parts. It avoids manual trigonometric conversion and reduces entry mistakes.
5. Why might the resultant angle be negative?
A negative angle simply means the resultant lies below the positive X-axis under the chosen convention. Enable normalization to convert it into an equivalent positive principal angle.
6. Does the calculator work with radians?
Yes. You can choose degrees or radians for angle entry and reporting. The calculator also shows the normalized heading in both units after solving.
7. What does the Plotly graph show?
The graph plots each vector from the origin, the head-to-tail combination path, and the final resultant vector. This helps you visually confirm direction and relative size.
8. Can I use different velocity units?
Yes. The unit label is fully editable, so you can use m/s, km/h, ft/s, or any other consistent velocity unit for display and exports.