Vector Norm Calculator
Enter the components of an n-dimensional vector to compute its L2 (Euclidean), L1 (Manhattan), and L∞ (maximum) norms plus the unit vector.
Last updated:
Input
Enter each component of the vector. Separate them with commas, spaces, or new lines (e.g. 3, 4, 12).
Result
L2 norm (magnitude)
13
L1 norm
19
L∞ norm
12
Dimension
3
Components and unit vector
| Index | Component | Unit vector |
|---|---|---|
| 1 | 3 | 0.2308 |
| 2 | 4 | 0.3077 |
| 3 | 12 | 0.9231 |
How it works
- The L2 norm (Euclidean norm) is the square root of the sum of squared components, √(Σxᵢ²). It equals the straight-line distance from the origin to the tip of the vector (the vector's magnitude).
- The L1 norm (Manhattan norm) is the sum of the absolute values of the components, Σ|xᵢ|, corresponding to distance traveled along a grid.
- The L∞ norm (maximum norm) is the largest absolute value among the components, max|xᵢ|.
- The unit vector is obtained by dividing each component by the L2 norm; it points in the same direction but has magnitude 1. A zero vector (all components 0) has an L2 norm of 0, so its unit vector is undefined.
- Components may be separated by commas, spaces, or new lines, and the number of components entered becomes the dimension.
Reviews
Tell us what you think of this calculator.
Write a review
Found an incorrect result or a problem? Turn this on to report it.
Rating