Vector Cosine Similarity, Angular Distance & Euclidean L2 Norm Calculator

Compare two vectors using Cosine Similarity (A·B / ||A||·||B||) and L2 distance.

Cosine Similarity (cos θ)
0.99 similarity
Euclidean L2 Distance 0.62 L2
Angular Separation (θ) 6.65 deg
Vector Dot Product (A · B) 27.5 dot
Inputs
val
Vector A component 1.
val
Vector A component 2.
val
Vector A component 3.
val
Vector B component 1.
val
Vector B component 2.
val
Vector B component 3.
Results & Graph
Cosine Similarity (cos θ)
0.99 similarity
Euclidean L2 Distance
0.62 L2
Angular Separation (θ)
6.65 deg
Vector Dot Product (A · B)
27.5 dot

Cosine Similarity (cos θ)

Graph 1 • A1 Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 similarity 0.5 similarity 1.1 similarity 50%: 0.93 similarity 0.9 50% 75%: 0.97 similarity 1.0 75% 100%: 0.99 similarity 1.0 100% 125%: 1 similarity 1 125% 150%: 1 similarity 1 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Cosine Similarity (cos θ) 0.99 similarity Euclidean L2 Distance 0.62 L2 Angular Separation (θ) 6.65 deg Vector Dot Product (A · B) 27.5 dot
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Cosine Similarity (cos θ)0.99 similarityEuclidean L2 Distance0.62 L2Angular Separation (θ)6.65 degVector Dot Product (A · B)27.5 dot
Summary: Dot product is 27.5, Cosine Similarity is 0.9933 (angle 6.65°), and Euclidean L2 distance is 0.616.
Summary: Dot product is 27.5, Cosine Similarity is 0.9933 (angle 6.65°), and Euclidean L2 distance is 0.616.
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Formula & Mathematical Methodology: Cosine Similarity & L2 Systems Engineering Formula

cos(θ) = A·B||A|| × ||B||
L2Distance = √Σ(Ai − Bi)²
cos(θ) = (A·B) / (||A|| × ||B||); L2_Distance = √Σ(A_i − B_i)²
  • a1: A1 (val)
  • a2: A2 (val)
  • a3: A3 (val)
  • b1: B1 (val)
  • b2: B2 (val)
  • b3: B3 (val)

Rounding: Binary/decimal capacities and engineering metrics retain full floating-point precision and round to 2 decimal places.

Worked Example: Architecture Sizing Example: Cosine Similarity & L2

Compare two vectors using Cosine Similarity (A·B / ||A||·||B||) and L2 distance.

  1. Enter the workload parameters, model dimensions, or network link specifications.
  2. Compute the sizing equation: cos(θ) = (A·B) / (||A|| × ||B||); L2_Distance = √Σ(A_i − B_i)².
  3. Inspect the primary capacity metric, headroom buffers, and 3 SVG visualizations.
Result: Calculates Cosine Similarity & L2 via cos(θ) = (A·B) / (||A|| × ||B||); L2_Distance = √Σ(A_i − B_i)².

Frequently Asked Questions

How does the Vector Cosine Similarity, Angular Distance & Euclidean L2 Norm Calculator compute capacity?

It evaluates cos(θ) = (A·B) / (||A|| × ||B||); L2_Distance = √Σ(A_i − B_i)² directly in your browser and plots three custom SVG diagrams.

Can I compare different cluster or model configurations side by side?

Yes. Use the "Compare (0/3)" button in the results panel to pin up to three configurations.

Does this tool upload any of my architecture parameters?

No. All calculations run 100% client-side in your browser.

Mathematics & Statistics · Machine Learning & Evaluation

Vector Cosine Similarity, Angular Distance & Euclidean L2 Norm Calculator: inputs, method, and how to read the result

Compare two vectors using Cosine Similarity (A·B / ||A||·||B||) and L2 distance.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • A1: Vector A component 1.
  • A2: Vector A component 2.
  • A3: Vector A component 3.
  • B1: Vector B component 1.

What the calculation includes

With the default values shown, Cosine Similarity (cos θ) is 0.99 similarity. The calculation follows Cosine Similarity & L2 Systems Engineering Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing A1 from 3 val to 4 val changes Cosine Similarity (cos θ) from 0.99 similarity to 1 similarity. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard IEEE, IETF RFC, and GPU/cloud hardware sizing conventions.
  • Capacity planning estimate; benchmark under production traffic patterns before finalizing cluster or hardware procurement.

Scope: IEEE / IETF / Cloud Systems Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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