Vetor Unitário
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
û = v/|v|
About this calculator
The unit vector calculator allows you to find the unit vector in the same direction as a given vector. A unit vector has a magnitude of 1 and points in the same direction as the original vector. To calculate it, divide each component of the vector by its magnitude (norm). The formula is û = v / |v|, where v is the original vector and |v| is its magnitude.
The calculation is done in three steps: first, compute the magnitude of the vector using the square root of the sum of squares of its components. Then, divide each component by the magnitude. The result is a unit vector, often used to represent directions in physics, computer graphics, and engineering.
Use this calculator when you need to normalize a vector, for example, to determine directions of forces, velocities, or fields. It is also useful for simplifying calculations involving direction, such as dot products or projections. The calculator accepts 2D or 3D vectors.
Caution: ensure the vector is not zero (magnitude zero), as division by zero is undefined. Also, the precision of the result depends on the precision of the input values. In practical applications, rounding may cause small errors.
Frequently asked questions
What happens if the vector is zero?
If the vector is zero (0,0,0), its magnitude is zero and the unit vector cannot be calculated because it would involve division by zero.
How do I calculate the magnitude of a vector?
The magnitude is the square root of the sum of the squares of each component. For example, for (x,y,z), magnitude = sqrt(x² + y² + z²).
Can I use this calculator for 2D vectors?
Yes, it accepts both 2D (x,y) and 3D (x,y,z) vectors. Just enter the corresponding values.
What is the use of a unit vector?
Unit vectors represent pure directions without magnitude. They are used in physics (forces), computer graphics (lighting), and navigation.
Is the result always exact?
It depends on the precision of the input values. The calculator uses floating-point arithmetic, so small rounding errors may occur.