Angle Between Two Vectors Calculator
This calculator finds the angle between two vectors in two or three dimensions using the dot product formula, the standard method used in physics, engineering, computer graphics and data science whenever you need to know how much two directions differ. Choose whether you are working in 2D or 3D, then enter the x, y (and z) components of vector A and vector B, for example forces, velocities or surface normals. The calculator works out the dot product of the two vectors and their magnitudes (lengths), divides one by the other to get the cosine of the angle, then takes the arccos to return the actual angle. Results appear as the angle in degrees and radians, the dot product, and a plain-English relationship such as parallel, perpendicular, acute or obtuse, so you can see at a glance how the vectors are oriented to each other. A working panel below shows every step, the dot product, both magnitudes, their product, cos(theta) and the final theta, so you can check the arithmetic or learn the method rather than just read off a number. Because the angle depends only on direction, not size, scaling a vector up or down never changes the result. Watch for the zero vector: if either vector has no length, the angle is mathematically undefined and the calculator flags this rather than showing a false answer.
