Length of a vector

Online calculator for calculating the length of a vector with 2 elements

Calculate the length of a vector

Enter the vector whose length is to be calculated. Then press the Calculate button


Vector length calculator

VectorResult
=
Decimal places

More vector functions for 2 elements

Addition
Subtraction
Multiplication
Scalar Multiplication
Division
Scalar-Division
Scalar Product
Interpolation
Distance
Distance Square
Normalization
Length

Vector functions for 3 or 4 elements


Description to calculate the length of a vector

This article describes how to calculate the magnitude of a vector. The magnitude of a vector is its length and can be calculated using Pythagorean theorem. After that, the square of the hypotenuse is equal to the sum of the squares of the legs. The lengths of the legs correspond to the respective coordinates of the vector.

The following figure shows the vector \(\left[\matrix{4\\3}\right]\) in a plane.

The magnitude is the length of the vector, it corresponds to the length of the hypotenuse of a right triangle.

So the length can be calculated:

\(|v|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\)

The same procedure applies to vectors with more than two elements.

\(\left|\left[\matrix{1\\2\\2}\right]\right|=\sqrt{1^2+2^2+2^2}=\sqrt{1+4+4}=\sqrt{9}=3\)
\(\left|\left[\matrix{-4\\6\\-12}\right]\right|=\sqrt{(-4)^2+6^2+(-12)^2}=\sqrt{16+36+144}=\sqrt{196}=14\)
Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?