2D Vector Angle Calculator
The 2D Vector Angle Calculator helps you find the angle between two vectors in a two-dimensional plane. This is useful in physics, computer graphics, and geometry when analyzing directions, forces, or movement paths. Just input the x and y components of both vectors, and the calculator will determine the angle between them in degrees.
Calculate the Angle Between Two 2D Vectors
Angle Between Two 2D Vectors Formula
Where:
- \(\vec{A} \cdot \vec{B} = A_x \cdot B_x + A_y \cdot B_y\) is the dot product
- \(|\vec{A}| = \sqrt{A_x^2 + A_y^2}\) is the magnitude of vector A
- \(|\vec{B}| = \sqrt{B_x^2 + B_y^2}\) is the magnitude of vector B
- \(\theta\) is the angle between the two vectors in radians (convert to degrees if needed)
This formula calculates the angle between two vectors using the dot product and the magnitudes of the vectors. It returns the angle in radians, which is often converted to degrees using \(\theta^\circ = \theta \cdot \frac{180}{\pi}\). Common applications include determining the directional relationship between two objects or computing angles for simulations, animations, or mechanical systems. Accurate vector angle measurement is crucial in fields like robotics, gaming, and navigation.