What is the dot product?

The dot product (A · B) is the sum of the products of corresponding vector components: Ax*Bx + Ay*By (2D) or Ax*Bx + Ay*By + Az*Bz (3D). It returns a scalar, not a vector.

How does the dot product relate to the angle?

For unit vectors, A·B equals the cosine of the angle between them. For non-unit vectors, A·B = |A||B|cos(θ). Rearranging: θ = acos(A·B / (|A||B|)).

What does a positive vs negative dot product mean in games?

Positive means the vectors point in roughly the same direction (angle 90°). Game AI uses this to decide "in front" vs "behind".

What is scalar projection?

The scalar projection of A onto B is (A·B)/|B|. It tells you how much of vector A lies along the direction of B. Useful for computing components of velocity along a slope or surface normal.

Is the dot product commutative?

Yes. A·B always equals B·A. The order of operands does not affect the result.

Why is normalizing vectors important before using the dot product?

When both vectors are unit vectors (magnitude = 1), the dot product directly equals cos(θ), making angle computation cheap. Without normalization you must divide by both magnitudes, which adds two sqrt operations.

Vector Dot Product Calculator (Game Dev)

Name: Vector Dot Product Calculator (Game Dev)
Availability: InStock
Author: Nham Vu

Enter 2D or 3D vector components to compute the dot product, angle between vectors, and projection — with instant game dev context.

Dimensions

Vector A

Vector B

Angle Visualization

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Results Click a row to copy

Dot Product (A · B) —

Angle between A and B —

cos(θ) —

Scalar projection of A onto B —

Scalar projection of B onto A —

|A| (magnitude) —

|B| (magnitude) —

Formula Reference

A · B = Ax*Bx + Ay*By [ + Az*Bz in 3D ]

A · B = |A| |B| cos(θ)

θ = acos( A·B / (|A||B|) )

proj_BA = (A·B) / |B|

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Summary

Enter 2D or 3D vector components to compute the dot product, angle between vectors, and projection — with instant game dev context.

How it works

Choose 2D or 3D mode using the toggle.
Enter X, Y (and optionally Z) components for Vector A.
Enter components for Vector B.
Read the dot product, angle, projections, and relationship label instantly.
Click any result row to copy its value to your clipboard.

Use cases

Checking if an enemy is in front of the player using the dot product sign.
Computing specular lighting intensity between surface normal and light direction.
Determining if two vectors are perpendicular (dot product = 0).
Calculating the scalar projection of velocity onto a surface for friction or sliding.
Blending animations based on the angle between a character forward vector and movement direction.
Steering AI agents by comparing current heading to the target direction.
Implementing cone-of-vision field-of-view checks in top-down games.
Verifying vector math formulas during game physics debugging.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu