# Circle radius to encapsulate a grid

Lets say there are in total n by n grids.

What would the formula be for the radius of a circle, from the central position of the grids to cover the entire square?

• it depends on your grid. like if length of each square's side is $l$ then radius$=\frac{1}{2}\times$diagonal length of big square$=\frac{1}{2}\times \sqrt{2}\times(l+l+l+l+l)=\frac{1}{2}\times \sqrt{2}\times 5l$ Nov 28 '19 at 8:56
• If you know the coordinates of the center and the coordinates of the corner your arrow is pointing to, use the Pythagorean Theorem to compute the hypotenuse. What do you know about the grid? Nov 28 '19 at 13:43

If each grid is a square of side $$a$$, then the length of the side of the square formed by the $$n×n$$ grids is $$na$$. So the diagonal of this large square will be of length $$na\sqrt{2}$$, which is the diameter of the circle. (I.e. $$R=\frac{na\sqrt{2}}{2}$$)