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Vector Direction and Unit Vector Calculator — result sheet
Find a vector’s magnitude, direction angle, and unit-vector components from its x and y components.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: magnitude = √(x²+y²); angle = atan2(y,x); unit vector = (x/magnitude, y/magnitude).
The magnitude is the vector’s length, and atan2 gives a quadrant-safe direction from the positive x-axis. Dividing each component by the magnitude creates a unit vector in the same direction.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- x component — minimum -1000000000; maximum 1000000000
- y component — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| x component | 3 |
| y component | 4 |
Magnitude: 5; direction: 53.13°; unit vector: (0.6, 0.8).
Assumptions and limits
- The vector is nonzero and lies in a two-dimensional Cartesian coordinate system.
- The direction is measured counterclockwise from the positive x-axis and reported in degrees.
- Unit-vector components are dimensionless; the original components retain their input units.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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