Vector Magnitude Calculator

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

Vector Coordinates
Vector Coordinates

Magnitude:

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

Learn how we calculated this below

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 length (size). 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|= √((x2 – x1)² + (y2 – y1)² + (z2 – z1)²)

Using this modified formula, the magnitude |a| of vector a is equal to the square root of x2 minus x1 squared, plus y2 minus y1 squared, plus z2 minus z1 squared.

You can also use our cross product calculator or dot product calculator to multiply vectors.

Frequently Asked Questions

What is a vector with a magnitude of 1?

A Vector with a magnitude of 1 is known as a unit vector.

Is a vector equal to its magnitude?

A vector can be equal to its magnitude but is not always.

Can a vector have a negative magnitude?

A vector cannot have a negative magnitude. It can only have a positive magnitude.