From your post, what you describe as accuracy, seems to be a failure rate. (This does not matter for the margin of error, but it's something to keep in mind.) This margin of error you're talking about is known as a 'confidence interval' in statistics. For this particular application, you'll want confidence intervals for the binomial distribution: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval In this case, the 95% confidence interval is: 0.683 +- 1.96*sqrt(0.683*(1-0.683)/{number of trials}) = 0.683 +- 1.96*sqrt(0.683*(1-0.683)/477) = 0.683 +- 0.042 So, with 95% certainity you can say the failure rate is between 64.1% and 72.5% If you want to know, for example, how large your sample should be to know with 95% certainity, the failure rate within 1%, you solve 0.01/2 = 1.96*sqrt((0.683*(1-0.683))/n) (wolfram alpha says n=33269.9) Sorry but... What's sqrt? square root