Numbers
Rechner für Vektorkomponenten
Used by developers, writers, and creators worldwide.
A vector component calculator turns the x and y components of a two-dimensional vector into its magnitude, direction, and unit vector. Enter the horizontal and vertical components and it computes the length using the Pythagorean theorem, the direction angle measured from the positive x-axis in both degrees and radians, and the unit vector pointing the same way but scaled to length one. Vectors describe anything with both size and direction, such as velocity, force, displacement, and acceleration, so this conversion is everywhere in physics, engineering, and game development. Students use it to check vector homework, engineers to resolve forces, and programmers to normalise directions for movement and lighting. The angle uses a full-circle calculation so it is correct in every quadrant, and the tool handles the zero vector, whose direction is undefined. Use it to find a vector's length and heading or to produce a clean unit vector.
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How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter the x component of the vector.
- Enter the y component of the vector.
- Click Generate to compute its properties.
- Read the magnitude, angle, and unit vector.
Use Cases
- •Finding the magnitude and direction of a vector
- •Resolving a force or velocity into a single heading
- •Normalising a direction to a unit vector in code
- •Checking two-dimensional vector homework
- •Converting between component and polar form
Tips
- →Magnitude comes straight from the Pythagorean theorem.
- →The unit vector keeps direction but sets length to one.
- →Angle is measured anticlockwise from the positive x-axis.
- →The zero vector has no defined direction.
FAQ
how is the magnitude computed
It uses the Pythagorean theorem: the magnitude is the square root of the sum of the squares of the components. For a vector with components 3 and 4 the magnitude is exactly 5, a familiar right-triangle result.
what does the unit vector represent
The unit vector points in the same direction as your vector but has length one. It is obtained by dividing each component by the magnitude, and it is widely used to represent pure direction in graphics and physics.
why use a full-circle angle calculation
A simple inverse tangent cannot tell apart opposite directions. The tool uses a quadrant-aware calculation so the reported angle is correct for vectors pointing in any of the four quadrants, not just the first.
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