Unit Vector Calculator

Summary

A unit vector (also called a normalized vector) is a vector with magnitude equal to 1 that points in the same direction as the original vector. To find it, you divide each component of the vector by the vector's magnitude. This tool handles both 2D vectors (x, y) and 3D vectors (x, y, z), showing the magnitude and each resulting component.

How it works

1. Choose 2D or 3D mode using the toggle.
2. Enter the x, y (and optionally z) components of your vector.
3. Click "Calculate" or press Enter to compute.
4. The tool calculates the magnitude: ||v|| = sqrt(x² + y² + z²).
5. Each unit vector component is displayed: x/||v||, y/||v||, z/||v||.
6. Copy any result value with one click.

Use cases

• Finding a normalized direction vector for 3D graphics or game physics.
• Computing surface normals in computer graphics.
• Normalizing feature vectors before machine learning calculations.
• Checking homework answers for linear algebra assignments.
• Converting displacement vectors to pure direction in navigation.
• Physics problems requiring a direction-only representation of a force.

Frequently Asked Questions