Vector Magnitude Calculator
Find the magnitude, unit vector, direction angles, and component contribution of a 2D or 3D vector. Enter the vector components and calculate instantly.
Choose a two-dimensional or three-dimensional vector.
Add the x, y, and optional z component values.
See magnitude, unit vector, angles, and calculation steps.
Square each vector component, add the squared values, and take the square root. For a 3D vector, include the z component in the sum.
This non-zero vector points into Quadrant I and forms a 53.13° angle with the positive x-axis.
Vector magnitude is used in physics, engineering, computer graphics, navigation, robotics, data science, game development, and geometry to measure the length or strength of a vector.
A zero vector has magnitude 0 and does not have a defined direction or unit vector. Negative components affect direction but not the magnitude because each component is squared.
How do I calculate vector magnitude?
Square every component, add the results, and take the square root of the total.
Can vector components be negative?
Yes. Negative values change the vector direction but the magnitude remains nonnegative.
What is a unit vector?
A unit vector has magnitude 1 and is found by dividing each component by the original vector magnitude.
Does this calculator support 3D vectors?
Yes. Select 3D vector and enter x, y, and z components.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
This calculator is intended for educational, mathematical, scientific, and planning purposes. Verify critical engineering or professional calculations independently.
