Vector Norm Calculator

Enter a vector and choose a norm type — L1, L2, or L-infinity — to calculate its size.

How to Use the Vector Norm Calculator

Enter the x, y, and z components of a vector, then choose which norm to compute: L1, L2 (Euclidean), or L-infinity.

L1 norm:  |Ax| + |Ay| + |Az|
L2 norm:  √(Ax² + Ay² + Az²)
L∞ norm:  max(|Ax|, |Ay|, |Az|)

"Norm" is really a family of ways to measure a vector's size, not one fixed formula — L2 is the ordinary straight-line magnitude most people mean by "length," L1 sums the components' absolute values instead (the "taxicab" distance a car takes on a city grid, corners only, no diagonals), and L∞ just takes whichever single component is largest. All three agree that a vector of all zeros has size zero; they disagree on almost everything else.