Vector Angle Finder Calculator

Example	Vector A	Vector B	Dot Product	Angle (Degrees)	Use Case
1	(1, 0, 0)	(0, 1, 0)	0	90.000000	Perpendicular vectors
2	(2, 2, 0)	(4, 4, 0)	16	0.000000	Same direction
3	(3, 4, 2)	(5, 1, 6)	31	40.235006	General 3D comparison
4	(1, -1, 0)	(-1, 1, 0)	-2	180.000000	Opposite directions

Formula Used

Dot Product Formula
A · B = (Ax × Bx) + (Ay × By) + (Az × Bz)

Magnitude Formula
|A| = √(Ax² + Ay² + Az²)
|B| = √(Bx² + By² + Bz²)

Angle Formula
cos(θ) = (A · B) / (|A| × |B|)
θ = arccos[(A · B) / (|A| × |B|)]

This calculator evaluates the angle between two vectors by combining the dot product and magnitudes. It supports both 2D and 3D vectors, and it returns results in degrees and radians.

How to Use This Calculator

Select whether you want a 2D or 3D vector comparison.
Choose the angle unit you prefer for the main displayed result.
Enter the components for Vector A.
Enter the components for Vector B.
Click Find Angle to calculate the relationship between the vectors.
Review the angle, dot product, magnitudes, cross product, and graph.
Use the CSV or PDF buttons to export the result summary.

FAQs

1. What does this vector angle finder calculate?

It calculates the angle between two vectors using their components. It also shows the dot product, vector magnitudes, cosine value, cross product, and the supplementary angle for deeper interpretation.

2. Can I use this calculator for 2D vectors?

Yes. Choose 2D mode and enter x and y values. The z-components are treated as zero, so the same formula still works correctly.

3. Can I use negative vector components?

Yes. Negative values are valid in vector calculations. They affect direction and may produce acute, right, obtuse, or straight angles depending on the two vectors entered.

4. Why do I get an error for zero vectors?

A zero vector has magnitude zero. Since the angle formula divides by the product of magnitudes, the angle becomes undefined when either vector has zero length.

5. What is the difference between degrees and radians?

Degrees divide a full turn into 360 parts. Radians measure angles using arc length. This calculator provides both so you can use the format needed for your problem.

6. What does a dot product of zero mean?

A dot product of zero usually means the vectors are perpendicular, provided both vectors are non-zero. In that case, the angle between them is 90 degrees.

7. What does the graph show?

The graph draws both vectors from the origin. In 2D mode, it shows a planar arrow view. In 3D mode, it displays their spatial directions to help visualize the angle.

8. Can I export my results?

Yes. The calculator includes CSV and PDF export buttons. They save the current result summary so you can keep a record for homework, reports, or engineering notes.