Vector Magnitude Calculator
Discover the length of vectors in up to 5 dimensions! Input your vector coordinates and get instant magnitude results.
Visualize the formula, understand the steps, and easily copy your results.
Select the dimension of the vector space you are working with.
Enter Vector Coordinates:
Magnitude Result:
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Calculation Steps:
- Magnitude =
Understanding Vector Magnitude
The magnitude of a vector, also known as its length or norm, is a measure of its overall size in space. For a vector $$ \vec{v} = (v_1, v_2, ..., v_n) $$, it's calculated using the formula:
This calculator simplifies finding the magnitude for vectors in 2D, 3D, 4D, and 5D spaces. Just enter the coordinates, and we'll do the rest!
Why is Vector Magnitude Important?
- Physics & Engineering: Quantifies force, velocity, displacement.
- Navigation: Determines distance between points.
- Graphics & Games: Used in movement, collision detection, etc.
Example Scenarios:
- 2D Vector (3, 4): Magnitude = $$ \sqrt{3^2 + 4^2} = 5 $$.
- 3D Vector (1, 2, 2): Magnitude = $$ \sqrt{1^2 + 2^2 + 2^2} = 3 $$.
Learn more about vector magnitude on Wikipedia.
Quick Docs on Vector Magnitude
Vector magnitude, or length, is the size of a vector. For a vector $$ \vec{v} = (x, y) $$, it's $$ ||\vec{v}|| = \sqrt{x^2 + y^2} $$. It's used to measure distances and forces. This tool calculates it for up to 5 dimensions. Formula: $$ ||\vec{v}|| = \sqrt{\sum_{i=1}^{n} v_i^2} $$. Applications: Physics, navigation, graphics. Wikipedia