How to use this calculator
- Enter or choose vector.
- The magnitude |v| updates as you type. Use Copy result or Share to keep it.
Method
|v| = √(v₁² + v₂² + … + vₙ²); L1 = Σ|vᵢ|; L∞ = max|vᵢ|
- vᵢ
- the components of the vector
- n
- the number of components
Worked example
- Square the components: 4, 9 and 36.
- Add them: 4 + 9 + 36 = 49.
- Take the square root: √49 = 7.
The vector (2, 3, 6) has a magnitude of exactly 7.
What the result means
The magnitude is the straight-line length of the arrow. The L1 norm is the distance travelled along the axes (city blocks), and the L∞ norm is the largest single component.
Assumptions and limits
- Components are in an ordinary Cartesian (orthonormal) basis.
- For physical vectors, all components must be in the same unit for the length to make sense.
Questions
Is magnitude the same as distance?
The magnitude of B − A is the distance between points A and B. Use the distance calculator to enter two points directly.
Can a magnitude be negative?
No. It is a length, so it is zero for the zero vector and positive otherwise.