How to Find Angle Between Two Vectors in Python?

Python Tutorials

Summary: In this tutorial, you will learn to calculate the angle between two vectors using Python Programming language.

Getting the angle between two vectors returns the angle in radians between two vectors of equal dimension.

In Python, you can easily find angle using the numpy.across() method.

Use numpy.arccos() to get the Angle Between Two Vectors

import numpy as np

v_1 = [0, 1]
v_2 = [1, 0]

#unit of vectors
unit_v_1 = v_1 / np.linalg.norm(v_1)
unit_v_2 = v_2 / np.linalg.norm(v_2)

#dot product of vectors
dot_product =, unit_v_2)

#angle between two vectors
angle = np.arccos(dot_product)

print(angle)    #90 degrees in radian

Output: 1.57079632679

This method requires you to use lists to represent vectors.

In the program, we have used vector / np.linalg.norm(vector) to get the unit vector of vector. We did this for both vectors.

Then, we called, v2) method to get the dot product of the previous results v1 and v2.

Finally, we called np.arccos(x) method with the previous result as x to get the angle between the two original vectors.

So, this is how you can get the angle between two given vectors in Python.

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