# Vector Norm Calculator

Enter the vector components below to solve the L^{1}, L^{2}, and L^{∞} norm.

## Vector Norm:

𝓁_{1}: | |

𝓁_{2}: | |

𝓁_{∞}: |

### Steps to Solve

#### Solve the L^{1} Norm

^{1}norm is the sum of the vector component's absolute values

L^{1} = |x| + |y|

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the L^{2} Norm

^{2}norm is the vector magnitude, use the vector magnitude formula to solve

L^{2} = x² + y²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the L^{∞} Norm

^{∞}norm is the max value of the absolute value of the vector components

L^{∞} = max(|x|, |y|)

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

𝓁_{1}: | |

𝓁_{2}: | |

𝓁_{∞}: |

### Steps to Solve

#### Solve the 𝓁_{1} Norm

_{1}norm is the sum of the vector component's absolute values

𝓁_{1} = |x| + |y| + |z|

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the 𝓁_{2} Norm

_{2}norm is the vector magnitude, use the vector magnitude formula to solve

𝓁_{2} = x² + y² + z²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Solve the 𝓁_{∞} Norm

^{∞}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

## On this page:

## 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 𝓁_{1} Norm

The 𝓁_{1} 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.

### 𝓁_{1} Norm Formula

Since the 𝓁_{1} norm is the sum of the component’s absolute values, the formula for the 𝓁_{1} norm is:

𝓁_{1} = |x| + |y| + |z|

Thus, the 𝓁_{1} 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 𝓁_{2} Norm

The 𝓁_{2} norm is sometimes referred to as the Euclidean norm, and you can find it using the vector magnitude formula.

## 𝓁_{2} Norm Formula

The 𝓁_{2} 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 𝓁_{2} 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.