Vector Magnitude Calculator
Calculate the magnitude (length) of a vector from its components.
The length of a vector
A vector's magnitude is its length — how far its endpoint is from the origin — found by squaring each component, summing them, and taking the square root. This calculates the magnitude from the components you enter, in two dimensions, three, or more, so you get the length without doing the arithmetic by hand.
Enter the vector's components and its magnitude is calculated.
Where magnitude comes up
Vector magnitude appears constantly in graphics, games, physics and data work. It is how you find the distance between two points, the speed from a velocity vector, or the size of a force. In games it is behind everything from how fast something is moving to whether two objects are within range. A common companion step is normalising — dividing a vector by its magnitude to get a unit vector that keeps the direction but has length one, useful whenever you care about direction without size. The magnitude is the foundation those calculations build on.
Questions & answers
How is magnitude calculated?
By squaring each component, summing them, and taking the square root — the length from the origin to the vector's endpoint.
Where is vector magnitude used?
Graphics, games and physics — for distances, speeds, force sizes, and as the basis for normalising a vector to unit length.
Is anything uploaded?
No. The calculation happens in your browser.