Vector Magnitude Calculator
Calculate the magnitude and unit vector of any vector from its components.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Vector Magnitude Calculator
Enter the components of your vector separated by commas. The calculator computes the magnitude (Euclidean norm) and the unit vector.
- Enter components. Type the vector components separated by commas. For a 2D vector (3, 4), the magnitude is 5. For 3D, enter three values.
- Read the result. The magnitude is shown as the primary result. The unit vector (normalized to length 1) appears below.
- Any dimension. The calculator works for vectors of any dimension, not just 2D or 3D.
Magnitude = sqrt(v1^2 + v2^2 + ... + vn^2). The unit vector is each component divided by the magnitude.
About Vector Magnitude
The magnitude (or length, or norm) of a vector is the Euclidean distance from the origin to the point defined by its components. It is calculated using the generalized Pythagorean theorem. The unit vector has the same direction but a magnitude of 1, and is found by dividing each component by the magnitude. Vectors and their magnitudes are fundamental in physics (force, velocity, acceleration), computer graphics (normalization for lighting), machine learning (feature scaling), and many areas of engineering.
Frequently Asked Questions
What is the magnitude of a vector?
The magnitude is the length of the vector, calculated as sqrt(x^2 + y^2) in 2D or sqrt(x^2 + y^2 + z^2) in 3D. For example, the vector (3, 4) has magnitude 5.
What is a unit vector?
A unit vector has a magnitude of exactly 1. It preserves the direction of the original vector. To find it, divide each component by the magnitude.
Can this calculator handle more than 3 dimensions?
Yes. Enter as many comma-separated components as you need. The formula generalizes to any number of dimensions: magnitude = sqrt(sum of all components squared).