Dot Product Calculator

Compute the dot product, cosine similarity, and angle between two vectors

Example Results

1 examples

Compute a 3D dot product

Multiply matching components and add them to get the inner product.

{
  "result": {
    "dotProduct": 32
  }
}
View input parameters
{ "vectorA": "1, 2, 3", "vectorB": "4, 5, 6", "decimalPlaces": 6 }

Key Facts

Category
Math, Date & Finance
Input Types
text, number
Output Type
json
Sample Coverage
2
API Ready
Yes

Overview

The Dot Product Calculator is a mathematical utility designed to instantly compute the inner product, cosine similarity, and angle between two vectors. By simply inputting the comma-separated components of Vector A and Vector B, users can quickly obtain precise algebraic results for physics, computer graphics, or machine learning applications without manual calculations.

When to Use

  • •When you need to determine the angle or directional alignment between two vectors in 2D, 3D, or higher-dimensional space.
  • •When calculating cosine similarity to measure how closely related two data points or text embeddings are in machine learning.
  • •When solving physics problems involving work, force, and displacement where the inner product is required.

How It Works

  • •Enter the comma-separated components of your first vector into the Vector A field (e.g., 1, 2, 3).
  • •Input the corresponding components of your second vector into the Vector B field (e.g., 4, 5, 6).
  • •Adjust the decimal places setting if you require a specific level of precision for your results.
  • •The calculator instantly multiplies the matching components and sums them up, returning the dot product, cosine similarity, and angle.

Use Cases

Computer Graphics: Calculating lighting, shading, and surface normals by finding the angle between light rays and surfaces.
Data Science & AI: Measuring the similarity between two text embeddings or feature vectors using cosine similarity.
Physics & Engineering: Computing the mechanical work done by a force applied over a specific displacement vector.

Examples

1. Calculating Work Done in Physics

Physics Student
Background
A student is solving a mechanics problem where a force vector is applied to an object, causing a displacement vector.
Problem
Needs to find the total work done, which is the dot product of the force and displacement vectors.
How to Use
Enter the force components in Vector A and the displacement components in Vector B.
Example Config
Vector A: 15, -5, 10 | Vector B: 2, 4, 1
Outcome
The tool calculates the dot product (30 - 20 + 10 = 20), instantly providing the total work done.

2. Measuring Text Embedding Similarity

Data Scientist
Background
A data scientist is comparing two small feature vectors representing text documents to see how similar their meanings are.
Problem
Needs to compute the cosine similarity between the two multi-dimensional vectors.
How to Use
Paste the comma-separated values of the first embedding into Vector A and the second into Vector B, then set decimal places to 4.
Example Config
Vector A: 0.1, 0.3, 0.8, -0.2 | Vector B: 0.2, 0.1, 0.9, 0.0 | Decimal Places: 4
Outcome
The calculator returns the dot product and the cosine similarity score, indicating the semantic closeness of the documents.

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FAQ

What format should I use for the vectors?

Enter the vector components as comma-separated numbers, such as '1, 2, 3' or '0.5, -1.2, 4'.

Do the two vectors need to have the same number of dimensions?

Yes, both Vector A and Vector B must have the exact same number of components to calculate a valid dot product.

Can this calculator compute cosine similarity?

Yes, along with the dot product, the tool automatically calculates the cosine similarity and the angle between the two vectors.

What is the maximum number of decimal places I can set?

You can configure the output precision up to 10 decimal places using the Decimal Places setting.

Does this tool support negative numbers and decimals?

Absolutely. You can input positive, negative, and decimal values for any vector component.

API Documentation

Request Endpoint

POST /en/api/tools/dot-product-calculator

Request Parameters

Parameter Name Type Required Description
vectorA text Yes -
vectorB text Yes -
decimalPlaces number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-dot-product-calculator": {
      "name": "dot-product-calculator",
      "description": "Compute the dot product, cosine similarity, and angle between two vectors",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=dot-product-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]