$\begingroup$

Given Point A and Point B in 2D space, how can I find the angle Point B is from Point A? 0° can be any direction; it doesn't matter. For example, Point A is at (0, 10) and Point B is at (10, 20). The angle is 45° in this example (assuming 0° is up).

$\endgroup$

2 Answers

$\begingroup$

I believe that the accepted answer does not correctly solve the problem for many people visiting this question. I am doing 2D simulations and the answer above does not solve my problem. Imagine the following circle:

$\hskip1.8in$

Assume that the middle of the circle is point A. Point B is at some angle from A according to the angles of the circle (so 0°) is right.

$\hskip2in$The atan2 function is what you need!

$$ atan2(y, x) $$$\hskip3.2in$ Where

$$ y = y_B - y_A $$$$ x = x_B - x_A $$

Read more about it here.

$\endgroup$ 4 $\begingroup$

From what I understood about your question, you want to find the angle between two points given their coordinates. In that case, first find the slope of the line using the slope formula: $$m=\dfrac{y_2-y_1}{x_2-x_1}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are coordinates on the line. Next, use this formula: $$\tan(\theta)=m$$ where $\theta$ is the angle. Therefore, the angle $\theta$ equals: $$\theta=\tan^{-1}(m)$$

---

Let's use the points $(0,10)$ and $(10,20)$ as an example (you mentioned it in your question). The slope is: $$m=\dfrac{10-20}{0-10}$$ $$m=\dfrac{-10}{-10}$$ $$m=1$$ Now we will find $\theta$. $$\tan(\theta)=1$$ $$\theta=\tan^{-1}(1)$$ $$\theta=45^\circ$$

---

Note: The $\tan(\theta)=m$ formula only gives the angle facing the positive $x$-axis (i.e. facing the "right"). So for a negative slope, you should get an angle that is greater than $90^\circ$. $\endgroup$ 4

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy