Compute L1 (Manhattan), L2 (Euclidean), L-infinity, or Lp norms for 2D and 3D vectors.
Dimension
Norm type
L2 (Euclidean) norm
Calculation steps
Square each component: [9, 16]
Sum of squares: 25
Square root: √25 = 5
Also in Linear Algebra
Linear Algebra
A vector norm calculator measures the size of a vector using different metrics. The L2 (Euclidean) norm gives the standard length, L1 (Manhattan) sums absolute values, and L-infinity takes the maximum absolute component.
L1 norm: ||v||₁ = |v₁| + |v₂| + ... (Manhattan distance). L2 norm: ||v||₂ = √(v₁² + v₂² + ...) (Euclidean distance). L∞ norm: ||v||∞ = max(|v₁|, |v₂|, ...) (Chebyshev distance).
The general Lp norm is (Σ|vᵢ|^p)^(1/p). L1 and L2 are special cases with p=1 and p=2.
Frequently asked questions
L2 is the most common for measuring distance. L1 is used in optimization (LASSO regression). L-infinity is used when you care about the worst-case component.
No — all norms are non-negative by definition. A norm of zero means the vector is the zero vector.
Related
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