↗️2D Vector Calculator

Calculate 2D vector addition, subtraction, dot product, magnitude, and angle

Vector A (ax, ay)

Vector B (bx, by)

How to Use the 2D Vector Calculator

Enter the components of vectors A(ax, ay) and B(bx, by) to instantly get magnitude, addition, subtraction, dot product, cross product, and the angle between them.

Key Formulas

Magnitude: |A| = √(ax² + ay²)

Dot product: A·B = ax·bx + ay·by

Cross product (2D scalar): A×B = ax·by − ay·bx

Angle: θ = arccos(A·B / (|A|·|B|))

FAQ

What if I enter a zero vector?

A zero vector has no direction, so the angle between it and another vector is undefined. The calculator will display "Undefined (zero vector)".

How do I get the unit vector?

Unit vector = A / |A| = (ax/|A|, ay/|A|). Divide each component by the magnitude shown in the results.