# How can I find the angle between two vectors, including directional information?

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Sebastian Echeverri
on 24 Feb 2015

Edited: AKASH KUMAR
on 20 May 2024 at 3:24

Hello, I am a graduate student, and I am working on a script that tracks the position of animals during a courtship. I have position data in the form of XY coordinates from two points on each animal's body taken from top down filming. I use these two points to create a vector that defines the animal's orientation. My script needs to calculate the angle between these two vectors, but also include directional information - IE, go from -180 through 0 to 180 degrees, depending on where the vectors are placed (see image).

This is the code that I currently have. It gives me the desired angle (I believe), but is NOT directional. 60 degrees to either side spits out as 60 degrees no matter which it is.

angle_maleToFemale_radians = acos(dot(maleFemaleVector,femaleVector)/(norm(maleFemaleVector)*norm(femaleVector))); angle_maleToFemale_degrees(index) = radtodeg(angle_maleToFemale_radians); angle_maleToFemale_degrees(index) = 180 - angle_maleToFemale_degrees(index);

##### 1 Comment

AKASH KUMAR
on 19 May 2024 at 18:29

Edited: AKASH KUMAR
on 20 May 2024 at 3:24

### Accepted Answer

Roger Stafford
on 24 Feb 2015

Edited: Roger Stafford
on 24 Feb 2015

If v1 = [x1,y1] and v2 = [x2,y2] are the components of two vectors, then

a = atan2d(x1*y2-y1*x2,x1*x2+y1*y2);

gives the angle in degrees between the vectors as measured in a counterclockwise direction from v1 to v2. If that angle would exceed 180 degrees, then the angle is measured in the clockwise direction but given a negative value. In other words, the output of 'atan2d' always ranges from -180 to +180 degrees.

One further observation: Besides the greater range of 'atan2d' as compared with 'acosd', the former does not suffer the inaccuracies that occur with 'acosd' for angles near zero and 180 degrees.

##### 14 Comments

Cenker Canbulut
on 31 Jul 2020

Edited: Cenker Canbulut
on 3 Aug 2020

Executed formula and works like charm! Thank you math! Thank you Roger Stafford!

Seth Wagenman
on 31 Jul 2020

Here is the link to my file developed in response to the same need in the 3-D case:

### More Answers (2)

Yashar Farajpour
on 17 Apr 2020

Edited: Yashar Farajpour
on 17 Apr 2020

You can use subspace function.

A = [x1,y1,z1];

B = [x2,y2,z2];

Angle = subspace(A',B')

%transposed! they must be column vectors

##### 0 Comments

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