Enter the x, y, and z coordinates into the calculator to determine the numerical length of the vector.

Numerical Length Formula

The following formula is used to calculate the numerical length of a vector in a 3-dimensional space.

L = sqrt(x^2 + y^2 + z^2)


  • L is the numerical length of the vectorx is the x-coordinate of the vectory is the y-coordinate of the vectorz is the z-coordinate of the vector

To calculate the numerical length of a vector, square each of the vector’s coordinates (x, y, and z), then add the results together. Finally, take the square root of the sum to get the numerical length.

What is a Numerical Length?

A numerical length refers to the measurement of the distance from one end to another of an object or space. It is a quantitative description of how long or short an object is, usually expressed in units such as inches, feet, centimeters, or meters. Numerical length can be measured using various tools like rulers, tape measures, or laser distance meters, depending on the size of the object or space being measured.

How to Calculate Numerical Length?

The following steps outline how to calculate the Numerical Length using the given formula:

  1. First, determine the values of x, y, and z.
  2. Next, substitute the values of x, y, and z into the formula: L = sqrt(x^2 + y^2 + z^2).
  3. Finally, calculate the Numerical Length.
  4. After inserting the values and calculating the result, check your answer.

Example Problem:

Use the following variables as an example problem to test your knowledge:

x = 3

y = 4

z = 5