# Average Distance between N points in area A

I am attempting to do statistical distribution of a variable number of random points on a flat plane. Context, it's for 2d mapping a star chart for a roleplaying game, and I would like to provide a formula that is good enough without using calculus. I know from GURPS Space 4th edition, that on a 3d map, given volume V and systems N randomly distributed throughout the volume, that the average distance between neighbors will $$1.12*\sqrt[3]{\frac VN}$$, but so far I have found nothing that doesn't use calculus for the 2-dimensional version other than maybe $$\sqrt(\frac AN)$$, or $$\frac AN$$, which seems... too simple?