This sample size calculator takes the figures you already have and applies the relationship behind sample size calculations for you, giving confidence level, z score abs and sample size from margin of error, population, proportion estimate and z score.
What Is the Sample Size Calculator?
The sample size calculator turns a set of measurements into confidence level, z score abs and sample size, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Sample Size Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with margin of error set to 10, population set to 5, proportion estimate set to 2, the calculator returns margin of 10, and z score abs of 100, and prop of -1. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out confidence level?
Enter margin of error, population, proportion estimate and z score. The calculator then works through the relationship and reports confidence level, z score abs and sample size.
What does the sample size actually calculate?
It takes margin of error, population, proportion estimate and z score and converts them into confidence level, z score abs and sample size using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter margin of error?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.