How to Calculate Vector Magnitude
What is Vector Magnitude?
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).
Formula
Step-by-Step Guide
- 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|
Worked Examples
Frequently Asked Questions
What is Vector Magnitude?
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
How accurate is the Vector Magnitude calculator?
The calculator uses the standard published formula for vector magnitude. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Vector Magnitude calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Vector Magnitude calculator use?
The core formula is: |v| = √(v₁² + v₂² + v₃² + ... + vₙ²) — Euclidean norm. Each step in the calculation is shown so you can verify the result manually.
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