the equation is Var(X)=np(1-p) n is the trial number, p is the probability of success.

Well, you can work it out by using the definition pretty easily. A couple of things to observe - 1) It increases with n so the more trials you have, the larger the variance of the number of successes. 2) It increases at the rate of n which means the Var(X/n) decreases with n at the rate of 1/n. This is because Var(X/n) = Var(x)/n^2 = np*(1-p)/n^2 = p*(1-p)/n. Since X/n would be the usual (and best) estimator of the success probability, this also seems reasonable. 3) If each trial is a Bernoulli r.v. then X/n = Sum(X[i])/n which means that we have an X-bar. That means we have a CLT (in fact the first CLT the DeMoivre-Laplace CLT) so the variance of X-bar = Var(X[i])/n and you could use this huge CLT hammer to back into the result. 4) It has its maximum at p=1/2 which should also seem right.