|v|Vector Magnitude Calculator
Works for any dimension: e.g. 3 4 or 1 2 3 or 1 2 3 4
The magnitude (or norm) of a vector is its length in Euclidean space, computed using the Pythagorean theorem generalised to any number of dimensions. The unit vector in the same direction is the vector divided by its magnitude. Magnitude is fundamental in physics (force, velocity, acceleration) and linear algebra (normalisation, distance, ML feature scaling).
- 1|v| = √(v₁² + v₂² + v₃² + ... + vₙ²) — Euclidean norm
- 2Unit vector: v̂ = v / |v| — magnitude 1, same direction
- 32D: |v| = √(x²+y²) — standard Pythagorean theorem
- 43D: |v| = √(x²+y²+z²)
- 5Distance between points A and B: |B−A|
v = (3, 4)=|v| = √(9+16) = √25 = 5Classic 3-4-5 Pythagorean triple
v = (1, 1, 1)=|v| = √3 ≈ 1.732; unit vector = (0.577, 0.577, 0.577)
| Norm | Formula | Name / Use |
|---|---|---|
| L1 (Manhattan) | Σ|vᵢ| | City-block distance, LASSO regularisation |
| L2 (Euclidean) | √(Σvᵢ²) | Standard length, Ridge regularisation |
| L∞ (Chebyshev) | max|vᵢ| | Chessboard distance |
| Lp (general) | (Σ|vᵢ|ᵖ)^(1/p) | Generalised norm |
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