Calculated Result
This result appears above the form after submission, with full working steps and graph.
Resultant Vector
Magnitude
Direction
Method
Step-by-step working
Plotly graph
Calculator Inputs
Example Data Table
| Vector | X Component | Y Component | Z Component | Magnitude | Direction |
|---|---|---|---|---|---|
| A | 3.00 | 4.00 | 0.00 | 5.00 | 53.13° |
| B | -2.00 | 5.00 | 0.00 | 5.39 | 111.80° |
| C | 1.00 | -3.00 | 0.00 | 3.16 | -71.57° |
| Resultant | 2.00 | 6.00 | 0.00 | 6.32 | 71.57° |
This sample uses direct components in 2D. The same method extends to 3D by including the z component.
Formula Used
1) Component addition
For vectors entered as components:
Rx = Σxi, Ry = Σyi, and in 3D Rz = Σzi.
2) Polar to component conversion for 2D
For magnitude M and angle θ:
x = M cos(θ) and y = M sin(θ).
3) Resultant magnitude
In 2D: |R| = √(Rx2 + Ry2)
In 3D: |R| = √(Rx2 + Ry2 + Rz2)
4) Resultant direction
In 2D: θ = atan2(Ry, Rx)
In 3D: azimuth = atan2(Ry, Rx), elevation = atan2(Rz, √(Rx2 + Ry2)).
How to Use This Calculator
- Select 2D or 3D based on the problem.
- Choose Components mode or Magnitude and angle for 2D work.
- Set the number of vectors you want to add.
- Enter a unit label if you want the output to display units.
- Fill in every visible vector field.
- Press Calculate Vector Sum to display the worked answer above the form.
- Review the step blocks, resultant values, and Plotly graph.
- Use the export buttons to download a CSV or PDF summary.
Tip: Use Load Example to populate a ready test case and verify the workflow quickly.
Frequently Asked Questions
What does this vector addition steps calculator do?
It adds multiple vectors, resolves components, shows each working step, calculates resultant magnitude and direction, and draws a Plotly graph for quick visual checking.
Can I solve both 2D and 3D vector problems?
Yes. Choose 2D for x and y work, or 3D for x, y, and z components. The calculator automatically updates the required inputs and outputs.
Can I enter vectors using magnitude and angle?
Yes, for 2D problems. Switch to polar input mode, enter magnitude and angle, and the calculator converts each vector into x and y components before summing.
How is the resultant magnitude calculated?
The tool first sums all x, y, and optional z components. It then applies the Euclidean magnitude formula using the final component totals.
Why does the calculator show running sums?
Running sums make the method transparent. You can inspect how each vector changes the partial result and quickly spot entry mistakes.
What angle convention is used here?
For 2D direction, the angle is measured from the positive x-axis using atan2. You can view or enter angles in degrees or radians.
What does the graph represent?
The graph plots head-to-tail vector addition and the final resultant from the origin. This helps confirm sign, direction, and overall geometry visually.
Can I download the solution?
Yes. After calculation, use the CSV button for data export and the PDF button for a compact summary of settings, vectors, and final results.