Angle Between Two Vectors

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Calculate the angle between two vectors in 2D or 3D space.

Vector A

Vector B

Calculation Results

90.00°

Angle (Degrees)

Angular separation between vectors

Angle (Radians)1.5708rad

Dot Product0.00

Magnitude |A|1.00

Magnitude |B|1.00

About this calculator

Understanding Vector Angles

The angle between two vectors is the angle formed at the intersection of their directions. It is calculated using the dot product formula: A · B = |A||B| cos(θ). This relationship is fundamental in physics for calculating work, projection, and directional alignment.

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Pro Tips

The result will always be between 0 and 180 degrees (0 and π radians).
If the dot product is 0, the vectors are orthogonal (90 degrees).
If the angle is 0, the vectors are parallel and point in the same direction.
If the angle is 180, the vectors are parallel and point in opposite directions.

Fun Facts

"In game development, the dot product is used to determine if an enemy is facing the player."
"In machine learning, 'Cosine Similarity' (closely related to the angle) is used to find similar documents or products."
"The concept works in any number of dimensions, not just 2D or 3D!"

Formula: θ = arccos((A · B) / (|A| |B|))