Unit Vector Calculator
Enter the components of any vector to find its unit vector — the vector of length 1 pointing in the same direction.
Unit vector: (0.6, 0.8)
- 1
Sum of squared components
3² + 4² = 25 - 2
Magnitude |v|
√(25) = 5Euclidean length; dividing each component by this gives the unit vector.
How does this calculator work?
A unit vector is a vector of length 1 pointing in a given direction. To find it, compute the magnitude |v| = √(sum of squared components), then divide each component by |v|. The zero vector cannot be normalized because its magnitude is zero.
Formula
How this is calculated
Enter the vector components separated by spaces or commas; the calculator accepts vectors of any dimension (2D, 3D, or higher). Each value is parsed as a number, so non-numeric entries are rejected.
The magnitude (Euclidean norm) is computed as |v| = √(Σ vᵢ²), the square root of the sum of the squared components. The unit vector û is then formed by dividing every component by this magnitude: ûᵢ = vᵢ / |v|. By construction û points in the same direction as v but has length exactly 1, which you can verify since √(Σ ûᵢ²) = 1.
The zero vector (all components 0) has magnitude 0 and cannot be normalized, since dividing by zero is undefined — in that case no result is returned. The unit vector is dimensionless; if the input has physical units, the unit vector simply encodes direction. The 2D plot draws the original vector and its normalized counterpart from the origin so you can see they share a direction.
Frequently asked questions
A unit vector has a magnitude (length) of exactly 1. It is obtained by dividing each component of a vector by the vector's magnitude, preserving direction while standardizing length.
No. The zero vector has magnitude 0, and normalizing requires dividing by the magnitude. Division by zero is undefined, so the zero vector has no unit vector.
Yes. Enter any number of components separated by spaces or commas. The magnitude and unit vector are computed for vectors of any dimension; the plot is shown only for the first two components.
Also known as
TG we-Calculate Editorial Team. (2026). Unit Vector Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/unit-vector-calculator
TG we-Calculate Editorial Team. "Unit Vector Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/unit-vector-calculator.
TG we-Calculate Editorial Team, "Unit Vector Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/unit-vector-calculator
@misc{wecalculate_unit_vector_calculator, title = {Unit Vector Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/unit-vector-calculator}}, year = {2026}, note = {TG we-Calculate} }
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