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Three-Dimensional Cosine Similarity Calculator — result sheet
Calculate dot product, cosine similarity, and the angle between two three-dimensional vectors.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: cosine similarity=(A·B)/(||A||||B||); angle=arccos(similarity).
The vector norms are shown through the dot-product and angle outputs, while the cosine stays unitless.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector A x — minimum -1000000; maximum 1000000
- Vector A y — minimum -1000000; maximum 1000000
- Vector A z — minimum -1000000; maximum 1000000
- Vector B x — minimum -1000000; maximum 1000000
- Vector B y — minimum -1000000; maximum 1000000
- Vector B z — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vector A x | 1 |
| Vector A y | 2 |
| Vector A z | 3 |
| Vector B x | 3 |
| Vector B y | 2 |
| Vector B z | 1 |
Dot product =10; cosine similarity ≈0.7143; angle ≈44.42°.
Assumptions and limits
- Both vectors have finite components and neither is the zero vector.
- The angle is reported in degrees and the similarity is clamped only for floating-point safety.
- No statistical or semantic meaning is inferred from the similarity value.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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