Calculated Result
Your average vector appears here after submission.
Calculator
Use one vector per line. The result is shown above this form.
Plotly Graph
Input vectors and the computed average are drawn from the origin.
Detailed Output Table
Example Data Table
| Label | X | Y | Z | Weight |
|---|---|---|---|---|
| V1 | 3.5 | 4.2 | 1.1 | 1 |
| V2 | 5 | 2.1 | 0.5 | 1.3 |
| V3 | 1.8 | 6.4 | 2 | 0.9 |
| V4 | 4.4 | 3.3 | 1.7 | 1.1 |
Use the example button to load these values into the calculator instantly.
Formula Used
Simple vector average
A = (V₁ + V₂ + ... + Vₙ) / n
Weighted vector average
A = (w₁V₁ + w₂V₂ + ... + wₙVₙ) / (w₁ + w₂ + ... + wₙ)
Magnitude of the average vector
|A| = √(Ax² + Ay²) for 2D, or √(Ax² + Ay² + Az²) for 3D
2D direction
θ = atan2(Ay, Ax)
3D direction
Azimuth = atan2(Ay, Ax), Elevation = atan2(Az, √(Ax² + Ay²))
How to Use This Calculator
- Choose whether your dataset contains 2D or 3D vectors.
- Paste one vector per line into the vector field.
- Select auto, comma, or space separation.
- Enable weighted averaging only if each vector has a matching weight.
- Pick your preferred angle output and decimal precision.
- Press the calculate button to show results above the form.
- Review the summary cards, graph, and detailed table.
- Use the export buttons to save your result as CSV or PDF.
Frequently Asked Questions
1. What does a vector average represent?
It represents the central direction and component balance of a vector set. Unlike averaging only magnitudes, it preserves direction on each axis and shows the net tendency of the dataset.
2. When should I use weighted averaging?
Use weighted averaging when some vectors should influence the result more strongly. Common examples include confidence scores, time duration, mass contribution, sample importance, or repeated measurements with different reliability.
3. Can this calculator handle both 2D and 3D vectors?
Yes. Select 2D for x and y values, or 3D for x, y, and z values. The form, direction output, table columns, and graph update automatically.
4. Why can the average magnitude be smaller than individual magnitudes?
Vectors pointing in different directions can partially cancel each other. That cancellation reduces the final average magnitude even when the original vectors each have large individual lengths.
5. What is the difference between resultant and average vector?
The resultant is the direct sum of all vectors. The average vector is that total divided by the number of vectors, or by total weight in weighted mode.
6. What separators are accepted in the input?
Auto detect accepts commas, spaces, and tabs. You can also force comma mode or space mode from the separator menu when your dataset uses a consistent format.
7. Does the calculator show vector direction?
Yes. For 2D, it shows the average angle from the positive x-axis. For 3D, it reports azimuth and elevation using the computed average vector components.
8. What do the export options include?
CSV export includes summary values and row-by-row vector details. PDF export includes the same information in a clean report format that is useful for records, coursework, and review.