Unit Vector Calculator

Summary

Enter a 2D or 3D vector and instantly get its unit vector, magnitude, and step-by-step normalization.

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