# Vector Magnitude Calculator

Calculate the magnitude of a vector by entering the two-dimensional or three-dimensional coordinates below.

## Magnitude:

### Steps to Solve

#### Use the Vector Magnitude Formula

|a| = x² + y²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

### Steps to Solve

#### Use the Vector Magnitude Formula

|a| = x² + y² + z²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

## On this page:

## How to Find the Magnitude of a Vector

In linear algebra, vectors represent an ordered sequence of numbers. Vectors have both a direction and a magnitude.

So what exactly is the magnitude of a vector? The magnitude is the vector’s size, or length. In other words, it’s the distance between the vector’s initial point and end point.

A magnitude is always a positive number, it cannot be negative. The magnitude of a vector *a* is denoted *|a|*.

### Vector Magnitude Formula

The magnitude of a vector is equal to the square root of the sum of the squares of each component of the vector. So, the vector formula looks like this:

|a|= x² + y² + z²

Thus, the magnitude *|a|* of vector *a* is equal to the square root of the sum of the square of each of the vector’s components *x*, *y*, and *z*.

If you know the initial and end points of the vector, you can modify the formula like this to solve for its magnitude:

|a|= √((x_{2} – x_{1})² + (y_{2} – y_{1})² + (z_{2} – z_{1})²)

Using this modified formula, the magnitude *|a|* of vector *a* is equal to the square root of *x _{2}* minus

*x*squared, plus

_{1}*y*minus

_{2}*y*squared, plus

_{1}*z*minus

_{2}*z*squared.

_{1}You can also use our cross product calculator or dot product calculator to multiply vectors.