Norm Calculator
Compute L1, L2 (Euclidean), and L-infinity norms of a vector.
Inputs
L2 Norm (Euclidean)
5.000000
L1 Norm (Manhattan)
7.000000
L∞ Norm (Maximum)
4.000000
Step by step
Vector
= [3, -4, 0]
L1 = Σ|vᵢ|
= 7
L2 = √(Σvᵢ²)
= 5
L∞ = max|vᵢ|
= 4
How it works
A norm measures the 'length' or 'size' of a vector. The L2 (Euclidean) norm is the ordinary distance from the origin. The L1 (Manhattan) norm sums absolute values. The L∞ (Chebyshev) norm is the maximum absolute component.
Formulas
L2 (Euclidean)
||v||₂ = √(Σ vᵢ²)
- v
- Input vector
L1 (Manhattan)
||v||₁ = Σ |vᵢ|
- v
- Input vector
L∞ (Maximum)
||v||∞ = max |vᵢ|
- v
- Input vector
Frequently Asked Questions
Which norm should I use?
L2 is the default geometric length. L1 is used in sparse optimization (lasso). L∞ is used in game theory and when bounding the worst-case component matters.
Is the L2 norm the same as magnitude?
Yes. The Euclidean norm is the standard vector magnitude — the straight-line distance from the origin to the vector's tip.