Math & Science100% Free Tool

Free Vector Dot Product & Angle Calculator (2D & 3D) Online

Calculate dot product (a · b), vector magnitudes (|a|, |b|), unit vectors, and angle θ between vectors in 2D and 3D space. — 100% free online utility, zero sign-up, zero paywalls, and private client-side processing.

100% Client-Side0ms Latency
Algebraic & Polynomial Solverax² + bx + c = 0
Roots of Equationx₁ = 3.000, x₂ = 2.000
Discriminant (Δ)1
Parabola Vertex(2.50, -0.25)
Axis of Symmetryx = 2.50

How It Works

1

Select Dimension

Choose 2D [x, y] or 3D [x, y, z].

2

Enter Vector Components

Input scalar coordinates for Vector A and Vector B.

3

Calculate Dot Product

Evaluates a · b = a₁b₁ + a₂b₂ (+ a₃b₃).

4

Inspect Angle Between Vectors

Formula: cos(θ) = (a · b) / (|a| × |b|).

Frequently Asked Questions

If a · b = 0 (and neither vector is zero), the two vectors are perpendicular (orthogonal) at exactly 90 degrees.

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