Vector Magnitude
Free Vector Magnitude calculator with clear step-by-step results.
About Vector Magnitude
The magnitude is the vector's length in 3D space.
Formula
Formula
|v| = √(x² + y² + z²)
Worked example
With the default values below, Vector Magnitude returns Magnitude of 5.000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- x component
- 3
- y component
- 4
- z component
- 0
Results
- Magnitude
- 5.000
- Unit Vector x
- 0.6000
- Unit Vector y
- 0.8000
Step by step
- 1Values used
- 2Formula
- 3Magnitude= 5.000
- 4Unit Vector x= 0.6000
- 5Unit Vector y= 0.8000
Assumptions and limits
- The result is derived only from the 3 inputs 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 4 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
How does this calculator work?
The magnitude is the vector's length in 3D space.
Why does this matter?
The unit vector points the same way with length 1.