Math
Distance between two points
Measure straight-line distance between two Cartesian points.
Calculators / Math / Three-dimensional vector magnitude
Three-dimensional vector magnitude calculator
Calculate the length of a three-dimensional vector.
On this page
Magnitude7units
Calculator controls
How to calculate
Calculate the length of a three-dimensional vector.
Magnitude = sqrt(x^2+y^2+z^2)
Worked example
X component: 2; Y component: 3; Z component: 6.
Magnitude: 7 units.
Assumptions and limits
No. Reversing a vector changes its direction but preserves its length. All three components must use matching units.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Magnitude is the length of a vector in an orthogonal three-dimensional coordinate system. Squaring the components removes their individual signs.
When this tool is useful
Calculate the length of a three-dimensional vector.
Understanding your inputs
| Input | What to enter |
|---|---|
| X component | Enter a number of at least -1000000000 and no more than 1000000000. |
| Y component | Enter a number of at least -1000000000 and no more than 1000000000. |
| Z component | Enter a number of at least -1000000000 and no more than 1000000000. |
Frequently asked questions
Does changing all component signs change magnitude?
No. Reversing a vector changes its direction but preserves its length. All three components must use matching units.