Vector Calculator

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

Example Results

1 examples

Add two 3D vectors

Combine two 3D vectors component by component.

{
  "result": {
    "vector": [
      5,
      7,
      9
    ]
  }
}
View input parameters
{ "vectorA": "1, 2, 3", "vectorB": "4, 5, 6", "operation": "add", "scalarValue": 2, "decimalPlaces": 6 }

Key Facts

Category
Math, Date & Finance
Input Types
text, select, number
Output Type
json
Sample Coverage
3
API Ready
Yes

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.

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.

Examples

1. Finding the Distance Between Two 3D Points

Game Developer
Background
A developer needs to find the exact distance between a player character and an enemy spawn point in a 3D environment.
Problem
Calculating the Euclidean distance between two 3D coordinate vectors.
How to Use
Enter the player's coordinates in Vector A and the enemy's coordinates in Vector B, then select 'Distance' as the operation.
Example Config
Vector A: 10, 15, 20 | Vector B: 3, 5, 8 | Operation: Distance
Outcome
The tool outputs the precise scalar distance between the two points in JSON format.

2. Scaling a Velocity Vector

Physics Student
Background
A student is modeling an object whose velocity suddenly doubles due to an applied force.
Problem
Multiplying a 2D velocity vector by a scalar value of 2.
How to Use
Input the initial velocity into Vector A, select 'Scalar Multiplication', and set the Scalar Value to 2.
Example Config
Vector A: 4.5, -2.1 | Operation: Scalar Multiplication | Scalar Value: 2
Outcome
The tool returns a new vector [9, -4.2] representing the doubled velocity.

3. Normalizing a Feature Vector

Data Scientist
Background
A machine learning model requires input features to be scaled to a unit length (magnitude of 1) to prevent larger values from dominating the algorithm.
Problem
Converting a raw multi-dimensional vector into a unit vector.
How to Use
Paste the comma-separated feature values into Vector A and choose the 'Normalize' operation.
Example Config
Vector A: 0.5, 1.2, 3.1, 0.8 | Operation: Normalize | Decimal Places: 4
Outcome
The calculator outputs the normalized vector components, ensuring the total magnitude equals exactly 1.

Try with Samples

math-&-numbers

Related Hubs

FAQ

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.

API Documentation

Request Endpoint

POST /en/api/tools/vector-calculator

Request Parameters

Parameter Name Type Required Description
vectorA text Yes -
vectorB text No -
operation select Yes -
scalarValue number No -
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-vector-calculator": {
      "name": "vector-calculator",
      "description": "Perform core vector operations such as addition, subtraction, scaling, magnitude, normalization, angle, and distance",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=vector-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]