Vector Calculator

Perform vector operations, calculations, and transformations. Free online vector calculator for physics and mathematics.

Calculator

Vector Calculator

Perform vector operations and calculations with our free online vector calculator. Add, subtract, multiply vectors, calculate magnitudes, and find angles between vectors.

Vector Calculator

Vector Operation

Vector A

Vector B

Result

Enter vector components above to see the calculation result.

Understanding Vectors

Vector Components

Vectors can be expressed in terms of their x, y, and z components in 3D space.

Magnitude

The magnitude (length) of a vector is calculated using the Pythagorean theorem.

Direction

The direction of a vector is specified by its components or by angles.

Operations

Vectors can be added, subtracted, and multiplied (dot and cross products).

How to Use

  1. Select the vector operation you want to perform
  2. Enter the components of Vector A (x, y, z)
  3. For binary operations, enter the components of Vector B
  4. Click "Calculate Vector Operation" to see the result
  5. Review the detailed calculation and explanation

Examples

Vector Addition:

A = (3, 4, 0), B = (1, 2, 0) → A + B = (4, 6, 0)

Dot Product:

A = (3, 4, 0), B = (1, 2, 0) → A · B = 11

Magnitude:

A = (3, 4, 0) → |A| = 5

Features

  • • Vector addition and subtraction
  • • Dot product calculation
  • • Cross product (3D vectors)
  • • Magnitude calculation
  • • Angle between vectors
  • • Free to use

Perfect For

  • • Physics calculations
  • • Engineering problems
  • • Mathematics students
  • • Computer graphics
  • • Mechanics problems
  • • Vector analysis

Frequently Asked Questions

What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. In physics and mathematics, vectors are used to represent quantities like force, velocity, and displacement.

How do I add vectors?

To add vectors, you can use the parallelogram law or component-wise addition. For 2D vectors, add corresponding x and y components separately.

What is the dot product?

The dot product (scalar product) of two vectors is a scalar value equal to the product of their magnitudes and the cosine of the angle between them.