# Vector Calculator

Perform core vector operations such as addition, subtraction, scaling, magnitude, normalization, angle, and distance

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

- **Category:** Math & Numbers

- **Keywords:** vector, magnitude, normalize, angle, distance, math

## Overview

The Vector Calculator is a precise mathematical utility designed to perform core vector operations instantly. Whether you need to add or subtract vectors, calculate magnitude, normalize directions, or find the angle and distance between two points, this tool handles multi-dimensional coordinates with ease. Simply input your vector components to get accurate, JSON-formatted results tailored to your specified decimal precision.

## Inputs

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

## When to use

- Calculating forces, velocities, or spatial distances in physics and engineering workflows.
- Normalizing directional vectors or computing angles for 3D graphics and game development.
- Determining the distance or similarity between data points in machine learning and data science.

## How it works

- Enter the components of your first vector (Vector A) as a comma-separated list, such as '1, 2, 3'.
- Select your desired mathematical operation, such as addition, magnitude, normalization, or angle.
- If required by the operation, provide a second vector (Vector B) or a scalar multiplier.
- Adjust the decimal places for precision and generate the exact mathematical result in JSON format.

## Use cases

- Game developers calculating the exact distance and normalized direction between a player and an object.
- Students and educators verifying manual linear algebra homework, such as vector addition or scalar multiplication.
- Data analysts computing the Euclidean distance or angle between multi-dimensional feature vectors.

## Frequently asked questions

### What vector dimensions are supported?

You can input vectors of any dimension (2D, 3D, or higher) by providing a comma-separated list of numbers. Both vectors must have the same number of dimensions for operations like addition, subtraction, or distance.

### How do I calculate the angle between two vectors?

Enter your first vector in Vector A, the second in Vector B, and select 'Angle' from the operation dropdown. The tool will compute the angle based on their dot product and magnitudes.

### What does the scalar value do?

The scalar value is used exclusively for the 'Scalar Multiplication' operation. It multiplies every component of Vector A by the number you specify.

### Can I control the precision of the results?

Yes, you can adjust the 'Decimal Places' setting to round your results to anywhere between 0 and 10 decimal places.

### What format are the results provided in?

The calculator outputs the results in a structured JSON format, making it easy to copy and integrate directly into your code or data pipelines.

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## Samples

- [Vector Database Samples](https://elysiatools.com/en/samples/vector-database): Comprehensive vector database examples including Chroma, Pinecone, Weaviate, FAISS, and custom vector solutions for semantic search and RAG applications
- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion