Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a circle with an arc beginning at point $(x,y)$. The radius is $r$, the arc angle(w/ respect to center) is $\theta$. How do I calculate the end point of the arc $(a,b)$ ?

I know that the arc-length=radius*(arc angle)

I can't seem to find an easy way to solve this, I think the way to go is with parametric equations but I'm not sure.

share|cite|improve this question
With the given information, all you can say is that $(a,b)$ is at a distance of $2r\sin(\theta/2)$ from $(x,y)$. What you need to pin the point down is some information about direction, for example: the slope of the tangent to the arc at $(x,y)$, or the slope of the line segment joining $(x,y)$ and $(a,b)$, or the angle with respect to the $x$-axis instead of the slope of either; that sort of thing. Do you see why? – Rahul Feb 6 '13 at 5:41

One way is to calculate the angle to the first point

$\alpha = \arctan \left ( \frac{p1.y-cp.y}{p1.x-cp.x} \right )$

Then you add your angle and calculate the new point:

$p2.x = cp.x + r * cos (\alpha +\theta )$

$p2.y = cp.y + r * sin (\alpha +\theta )$

enter image description here

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.