With this angle between two vectors calculator, you'll quickly learn how to find the angle between two vectors. It doesn't matter if your vectors are in 2D or 3D, nor if their representations are coordinates or initial and terminal points - our tool is a safe bet in every case. Play with the calculator and check the definitions and explanations below; if you're searching for the angle between two vectors formulas, you'll definitely find them there.
Since you're here, hunting down solutions to your vector problems, can we assume that you're also interested in vector operations? Check Omni's other tools at the coordinate geometry section.
Angle between two vectors formulas
In this paragraph, you'll find the formulas for the angle between two vectors - and only the formulas. If you'd like to understand how we derive them, go directly into the next paragraph, How to find the angle between two vectors.
Angle between two 2D vectors
Vectors represented by coordinates (standard ordered set notation, component form):
Also, it is possible to have one angle defined by coordinates, and the other defined by a starting and terminal point, but we won't let that obscure this section even further. All that matters is that our angle between two vectors calculator has all possible combinations available to you.
How to find the angle between two vectors?
OK, the above paragraph was a bit of a TL;DR. As a way of better understanding the formulas for the angle between two vectors, let's check where they come from:
Additionally, if your vectors are in a different form (you know their initial and terminal points), you'll need to perform some calculations beforehand. The aim is to reduce them into standard vector notation.
If your example vector is described by the initial point B=(x1,y1) and the terminal point B=(x2,y2), then vectora may be expressed as:
Still not making sense? No worries! We've prepared some exemplary calculations to make sure it's as clear as crystal.
Angle between two 3d vectors - example
Assume that we want to find the angle between two vectors: