Angle Between Vectors Calculator - Mathematical Calculations & Solutions
Vector 1
Vector 2
How It Works
Enter Vectors
Input components
Calculate Angle
Apply dot product
Common Examples
Angle Between Vectors Calculator
What It Does
Finds the angle between two vectors using their components. Works for both 2D and 3D vectors.
Why Use It
Helps in physics problems, computer graphics, engineering, and understanding directions in space.
Real Uses
Game development, robotics, navigation systems, and analyzing forces in physics.
Step-by-Step Examples
| Vector 1 | Vector 2 | Angle | Meaning |
|---|---|---|---|
| (1, 0) | (1, 0) | 0° | Same direction |
| (1, 0) | (0, 1) | 90° | Perpendicular |
| (1, 0) | (-1, 0) | 180° | Opposite direction |
| (3, 4) | (4, 3) | 16.26° | Small angle |
Frequently Asked Questions
What is the angle between vectors?
The angle between vectors is the smallest angle formed when two vectors meet at their starting point. It ranges from 0° to 180° and tells us how similar their directions are.
How do I enter vector components?
Enter the x, y, and z (if 3D) components of each vector. For example, vector (3,4) has x=3 and y=4. Use positive or negative numbers as needed. Make sure to put each number in the correct box.
What's the difference between 2D and 3D vectors?
2D vectors have only x and y components (like on a flat paper). 3D vectors also have a z component (like in real space with height). Choose 2D for flat problems and 3D for space problems.
Should I use degrees or radians?
Use degrees for everyday problems (easier to understand - like 90° for a right angle). Use radians for advanced math, physics, or programming (more precise for calculations). Most people prefer degrees.
How accurate are the results?
The calculator is very accurate and shows results to 4 decimal places. This is more than enough for most practical applications including homework, engineering, and scientific calculations.