Módulo de Vetor
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
|v| = √(x²+y²+z²)
About this calculator
The vector magnitude calculator computes the length (or magnitude) of a vector in three-dimensional space. The magnitude is obtained by the square root of the sum of the squares of its components: |v| = √(x² + y² + z²). This tool is useful for students, engineers, and professionals who need to quickly determine the intensity of a vector quantity.
To use the calculator, simply enter the x, y, and z coordinates of the vector in the designated fields. The result is displayed instantly, showing the magnitude value. The same formula applies for vectors in the plane (set z to 0) or in three-dimensional space.
Vector magnitude is used in various fields such as physics (to calculate resultant velocity, resultant force), engineering (structural analysis), and computer graphics (vector normalization). It is important to note that magnitude is always a non-negative value.
Be careful when entering coordinates: ensure you use the correct decimal separator (period or comma, depending on your region). Also, remember that the magnitude does not depend on the vector's direction, only on its magnitude.
Frequently asked questions
What does the magnitude of a vector mean?
The magnitude of a vector represents its length or size, i.e., the distance from the origin to the point defined by the vector in space.
Can I use this calculator for two-dimensional vectors?
Yes, simply enter the x and y coordinates and set z to 0. The result will be the magnitude of the vector in the plane.
Can the magnitude of a vector be negative?
No, the magnitude is always a non-negative value because it represents a distance.
What is the difference between magnitude and norm of a vector?
Magnitude and norm are synonyms; both refer to the length of the vector.
How do I calculate the magnitude of a vector from its components?
Use the formula |v| = √(x² + y² + z²), where x, y, and z are the components of the vector.