Vector Norm Calculator

Enter the vector components below to solve the L1, L2, and L norm.

Vector Coordinates
Vector Coordinates

Vector Norm:

𝓁1:
 
𝓁2:
 
𝓁:
 

Steps to Solve

Solve the 𝓁1 Norm

The 𝓁1 norm is the sum of the vector component's absolute values

𝓁1 = |x| + |y| + |z|

Substitute Values and Solve

Enter vector coordinates above to see the solution here

Solve the 𝓁2 Norm

The 𝓁2 norm is the vector magnitude, use the vector magnitude formula to solve

𝓁2 = x² + y² + z²

Substitute Values and Solve

Enter vector coordinates above to see the solution here

Solve the 𝓁 Norm

The L norm is the max value of the absolute value of the vector components

𝓁 = max(|x|, |y|, |z|)

Substitute Values and Solve

Enter vector coordinates above to see the solution here

Learn how we calculated this below


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How to Find Vector Norm

In Linear Algebra, a norm is a way of expressing the total length of the vectors in a space. Commonly, the norm is referred to as the vector’s magnitude, and there are several ways to calculate the norm.

How to Find the 𝓁1 Norm

The 𝓁1 norm is the sum of the vector’s components. This is sometimes referred to as a taxicab norm since it is equal to the path a taxi might take to get from the origin point to the vector’s coordinates.

𝓁1 Norm Formula

Since the 𝓁1 norm is the sum of the component’s absolute values, the formula for the 𝓁1 norm is:

𝓁1 = |x| + |y| + |z|

Thus, the 𝓁1 norm is equal to the absolute value of x plus the absolute value of y plus the absolute value of z.

How to Find the 𝓁2 Norm

The 𝓁2 norm is sometimes referred to as the Euclidean norm, and you can find it using the vector magnitude formula.

𝓁2 Norm Formula

The 𝓁2 norm is equal to the square root of the sum of the squares of each component of the vector. The formula looks like this:

|a|= x² + y² + z²

Thus, the 𝓁2 norm of a vector is equal to the square root of the sum of the square of each of the vector’s components x, y, and z.

How to Find the 𝓁 Norm

The 𝓁 norm is equal to the absolute value of the largest magnitude of each of the vector’s components. Thus, the 𝓁 norm is equal to the largest component value in the vector.

You’ll probably also be interested in our vector calculator.