Norm Calculator
Compute L1, L2 (Euclidean), and L-infinity norms of a vector.
About Norm Calculator
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
Worked example
With the default values below, Norm Calculator returns L2 Norm (Euclidean) of 5.000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Vector (comma or space separated)
- 3, -4, 0
Results
- L2 Norm (Euclidean)
- 5.000000
- L1 Norm (Manhattan)
- 7.000000
- L∞ Norm (Maximum)
- 4.000000
Step by step
- 1Vector= [3, -4, 0]
- 2L1 = Σ|vᵢ|= 7
- 3L2 = √(Σvᵢ²)= 5
- 4L∞ = max|vᵢ|= 4
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.