Vector Magnitude and Unit Vector
Find vector length and the normalized direction of a nonzero vector.
Your numbers
Magnitude
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
Use M = √(x²+y²+z²) and u = (x/M,y/M,z/M). x, y and z are vector components, M is magnitude, and u is the unit direction. The vector must be nonzero.
Find vector length and the normalized direction of a nonzero vector.
Worked example
- x component
- 3
- y component
- 4
- z component
- 0
- Magnitude
- 5
- Unit vector x
- 0.6
- Unit vector y
- 0.8
- Unit vector z
- 0
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: edc30398897a · Example checked: