# Dot Product Calculator

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

> Canonical page: https://elysiatools.com/en/tools/dot-product-calculator

- **Category:** Math & Numbers

- **Keywords:** dot product, inner product, vector, cosine similarity, angle, math

## 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.

## Inputs

- **Vector A** (text): e.g. 1, 2, 3
- **Vector B** (text): e.g. 4, 5, 6
- **Decimal Places** (number)

## 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.

## Frequently asked questions

### 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.

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