Vector Norm Calculator

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

• 2D
• 3D

Vector a

x

y

Vector a

x

y

z

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Vector Norm:

Vector Norm:

𝓁1:
𝓁2:
𝓁∞:

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Steps to Solve

Solve the L¹ Norm

The L¹ norm is the sum of the vector component's absolute values

L¹ = |x| + |y|

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

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|)

Substitute Values and Solve

Enter vector coordinates above to see the solution here

Vector Norm:

𝓁1:
𝓁2:
𝓁∞:

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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 calculate this below

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By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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Reviewed by

Pateakia Heath, PhD

Pateakia has worked in education for 15 years and has three degrees, including a PhD, Master's degree, and Bachelor's degree. She specializes in mathematics.

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Cite As:

Sexton, J. (n.d.). Vector Norm Calculator. Inch Calculator. Retrieved July 16, 2025, from https://www.inchcalculator.com/vector-norm-calculator/

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 can be 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.