Vector Magnitude Calculator
Calculate the magnitude (length) of a vector
About this calculator
The Vector Magnitude Calculator computes the length or magnitude of a vector in 2D or 3D space using the Euclidean distance formula. This tool is essential for students, engineers, and scientists working with physics, mathematics, or computer graphics. Vector magnitude represents the distance from the origin to the vector's endpoint and is crucial for normalizing vectors, calculating forces, velocities, and determining the size of displacement in various applications.
How to use
Enter the vector components (x, y for 2D vectors or x, y, z for 3D vectors) into the input fields. The calculator will automatically compute the magnitude using the formula √(x² + y² + z²). The result shows the vector's length as a positive scalar value.
Frequently asked questions
What is vector magnitude?
Vector magnitude is the length or size of a vector, calculated as the distance from the origin to the vector's endpoint using the Pythagorean theorem.
Can I calculate magnitude for negative components?
Yes, vector components can be negative. The magnitude calculation squares each component, so negative values become positive in the final result.
What's the difference between 2D and 3D vector magnitude?
2D vectors use √(x² + y²) while 3D vectors use √(x² + y² + z²). The process is the same, just adding the z-component for 3D calculations.