Analyze weighted vectors across any dimension with clarity. Track magnitudes, components, and directional balance instantly. Make every weighted component decision clearer, faster, and smarter.
Use the responsive form below. It shows three columns on large screens, two on smaller screens, and one on mobile.
| Vector | C1 | C2 | C3 | Weight |
|---|---|---|---|---|
| V1 | 2 | 4 | 1 | 1 |
| V2 | 3 | 1 | 5 | 2 |
| V3 | 4 | 6 | 2 | 3 |
| Weighted Average | 3.5 | 4 | 2.8333 | 6 |
Component weighted average: A_d = (Σ(w_i × x_id)) / Σ(w_i)
Vector magnitude: |A| = √(Σ(A_d²))
Unit direction vector: U_d = A_d / |A|
Weighted variance by component: Var_d = Σ(w_i × (x_id − A_d)²) / Σ(w_i)
Reference cosine similarity: cos(θ) = (A · R) / (|A| × |R|)
Choose how many vectors you want to combine and set the number of components in each vector.
Enter each component value and assign a weight to every vector. Weights show how strongly each vector influences the final result.
Select an output mode for raw averages, unit direction, or percent composition. Add a reference vector if you want alignment checks.
Press submit to place the result above the form, inspect the graph, and export the calculated tables as CSV or PDF.
It gives one combined vector where each source vector influences the outcome according to its assigned weight. Larger weights pull the final vector closer to their components and direction.
Yes, but only when you enable the negative-weight option. Signed weights can model opposing influence, although variance metrics are less meaningful when weights are not all nonnegative.
The weighted average divides the weighted component sums by the total weight. When total weight is zero, the average becomes undefined and no stable result exists.
It converts the absolute component sizes of the average vector into percentages. This helps compare how strongly each component contributes to the overall combined vector profile.
Use it when direction matters more than size. The unit vector keeps the final direction while normalizing its magnitude to one, which is useful for orientation analysis.
It measures directional alignment between the average vector and your reference vector. Values near one indicate strong alignment, near zero indicate orthogonality, and negative values show opposing directions.
Yes. You can set the dimension count higher and the calculator will compute every component, magnitude, weighted variance, and a graph suitable for the selected dimension size.
CSV export creates spreadsheet-friendly text from the visible result tables. PDF export captures the result section and graph so you can save or share the formatted output.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.