What is the formula to calculate the distance (arc length) between 2 points ( x 1 , y 1 , z 1 ) and ( x 2 , y 2 , z 2 ) on the circumference of a circle of radius r without knowing the angle θ between them. I found that arc length can be calculated knowing θ. But I know only the x , y , z co-ordinates of 2 points on the circumference of a circle. Please suggest.

Question

What is the formula to calculate the distance (arc length) between 2 points   (      x    1    ,      y    1    ,      z    1    ) and   (      x    2    ,      y    2    ,      z    2    ) on the circumference of a circle of radius   r without knowing the angle   θ between them. I found that arc length can be calculated knowing   θ. But I know only the   x  ,  y  ,  z co-ordinates of 2 points on the circumference of a circle. Please suggest.

Myla Pierce · Accepted Answer

Let   d be the (straight-line) distance between the two points. Then the arclength between them is  s  =  2  r      sin          −      1        ⁡      (          d              2        r              )  Note that this does not assume that the circle is centered at the origin (as some of the others seem to do).

What is the formula to calculate the distance (arc length) between 2 points ( x 1

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