Calculateur de Norme de Vecteur
Calculez la norme (longueur ou norme euclidienne) d’un vecteur en 2D, 3D ou n-dimensions. Obtenez un calcul étape par étape montrant chaque composante au carré, la somme sous le radical et le résultat final de la racine carrée, avec un schéma vectoriel interactif.
Votre bloqueur de pubs nous empêche d’afficher des annonces
MiniWebtool est gratuit grâce aux annonces. Si cet outil vous a aidé, soutenez-nous avec Premium (sans pubs + outils plus rapides) ou ajoutez MiniWebtool.com à la liste blanche puis rechargez la page.
- Ou passez à Premium (sans pubs)
- Autorisez les pubs pour MiniWebtool.com, puis rechargez
Calculateur de Norme de Vecteur
The Vector Magnitude Calculator computes the length (Euclidean norm) of a vector in any number of dimensions. Enter your vector components and instantly get the magnitude, unit vector, direction angles, a detailed step-by-step square root computation, component contribution analysis, and an interactive diagram showing the vector and its projections.
The Magnitude Formula
For a vector \(\vec{v} = \langle v_1, v_2, \ldots, v_n \rangle\), the magnitude (or Euclidean norm) is:
$$|\vec{v}| = \sqrt{v_1^2 + v_2^2 + \cdots + v_n^2}$$
This is a direct generalization of the Pythagorean theorem. In 2D, \(|\vec{v}| = \sqrt{x^2 + y^2}\) gives the hypotenuse of the right triangle formed by the components. In 3D, it extends to \(|\vec{v}| = \sqrt{x^2 + y^2 + z^2}\).
Magnitude by Dimension
2D Vector
\(|\vec{v}| = \sqrt{x^2 + y^2}\)
The length of a vector in the xy-plane. Equivalent to the distance from the origin to point (x, y).
3D Vector
\(|\vec{v}| = \sqrt{x^2 + y^2 + z^2}\)
Used in physics, engineering, and 3D graphics for spatial calculations.
Unit Vector
\(\hat{v} = \frac{\vec{v}}{|\vec{v}|}\)
A vector with magnitude 1 pointing in the same direction. Used to represent pure direction.
n-Dimensional
\(|\vec{v}| = \sqrt{\sum_{i=1}^{n} v_i^2}\)
The same formula works in any dimension, used in data science and machine learning.
Key Formulas Reference
| Formula | Expression | Description |
|---|---|---|
| Magnitude | \(|\vec{v}| = \sqrt{\sum v_i^2}\) | Length of the vector (L2 norm) |
| Unit Vector | \(\hat{v} = \vec{v} / |\vec{v}|\) | Normalized direction vector |
| Direction Cosine | \(\cos \alpha_i = v_i / |\vec{v}|\) | Cosine of angle with each axis |
| Distance | \(d = |\vec{B} - \vec{A}|\) | Distance between two points |
Real-World Applications
How to Use the Vector Magnitude Calculator
- Select a dimension — choose 2D, 3D, or Custom for higher dimensions. Or click a quick example to auto-fill a sample vector.
- Enter components — type the vector components separated by commas (e.g.,
3, 4for 2D or1, 2, 3for 3D). Spaces, semicolons, and international number formats are also supported. - Click Calculate — press the "Calculate Magnitude" button to compute all results.
- Review results — see the magnitude, unit vector, direction angles, step-by-step formulas, component contribution breakdown, and the interactive vector diagram with toggleable layers.
Frequently Asked Questions
Citez ce contenu, cette page ou cet outil comme suit :
"Calculateur de Norme de Vecteur" sur https://MiniWebtool.com/fr// de MiniWebtool, https://MiniWebtool.com/
by miniwebtool team. Updated: 2026-04-10
Vous pouvez également essayer notre Résolveur Mathématique IA GPT pour résoudre vos problèmes mathématiques grâce à des questions-réponses en langage naturel.