Reproducing the answer
Find the magnitude, divide each component, and verify the new self-dot product equals one.
Math calculator
Unit Vector Calculator
Normalize a nonzero vector to magnitude one. Each submitted value produces unit direction vector plus the intermediate reasoning.
Unit Vector inputs
Start with the given values
Seeing the method in action
Normalizing (3,4,0) gives (0.6,0.8,0).
Problems this can answer
Unit directions separate orientation from scale in geometry, forces, projections, and bases. Unit Vector also relates to normalizing divisor.
How Unit Vector works
A unit vector preserves direction while dividing every component by the original magnitude. Unit Vector can be compared with target direction.
The calculation treats vector v according to their labels, not as interchangeable values in unit vector.
Checking the Unit Vector output
The zero vector cannot be normalized because it has no direction and division by its magnitude is impossible.
An impossible unit direction vector sign or magnitude usually points to field assignment before it points to rounding.
Using the result beyond this page
Start the unit vector setup by pairing every source number with vector v. Convert unlike units before typing, and postpone rounding until the displayed unit direction vector is ready to report.
Positive scaling leaves the unit direction unchanged; negative scaling reverses it. Use that direction of change to check the displayed unit direction vector before copying it elsewhere.
When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated unit direction vector from an unlabeled number and makes later checking substantially easier.
Vector magnitude supplies the required divisor. Keep that boundary in mind when interpreting the numerical result.
For later verification, record vector v before rounding the unit direction vector. The unrounded working value can feed subsequent steps while the rounded value serves presentation.
Checking length and direction
A reproducible Unit Vector result begins with Vector v. The reported vector should have magnitude one and remain parallel to the input; corresponding nonzero component ratios should agree.
For Unit Vector, keep unrounded components until the final magnitude or direction has been reported. Dot the reported unit vector with itself; the result should be one within rounding, while its direction remains parallel to the input.
Questions about Unit Vector
What does Unit Vector calculate?
A unit vector preserves direction while dividing every component by the original magnitude.
When is Unit Vector useful?
Unit directions separate orientation from scale in geometry, forces, projections, and bases.
What can make Unit Vector misleading?
The zero vector cannot be normalized because it has no direction and division by its magnitude is impossible.