Standard Error Question with regard to pi estimation using random numbers

My question here is about Standard Error. I am writing a program to calculate pi using pseudo-random numbers. The program works perfectly, however, I also want to display how reliable the number is. The formula I am using for Standard Error is sqrt(p(1-p)/N) where p is the probability my randomly picked point landed inside the circle, and N is the number of random points.

However, sometimes the error seems to be way off. For example, one time at 100 iterations: PI was estimated at 2.84 but standard error was only .045.

Someone please help me here.