# Sample Size Calculator

If you're conducting research and wonder **how many measurements you need so that it is statistically significant**, this sample size calculator is here to help you. All you need to do is ask yourself these three questions before you use it:

- How
**accurate**should your result be? (margin of error) - What
**level of confidence**do you need? (confidence level) - What is your
**initial estimate**? (proportion estimate)

Read on to learn **how to calculate the sample size** using this tool, and what do all the variables in the sample size calculation formula mean.

## Sample size calculation formula

The equation that our sample size calculator uses is:

`n₁ = Z² * p * (1-p) / ME²`

where:

`Z`

— The z-score associated with the**confidence level**you chose. Our statistical significance calculator calculates this value automatically (shown in`Advanced mode`

), but if you want to learn how to calculate it by hand, take a look at the instructions of our confidence interval calculator.`ME`

— Margin of error, also known as the**confidence interval**. It tells you that you can be sure (with probability of confidence level, for example 95%), that the real value doesn't differ from the one that you obtained by more than this percentage.`p`

— Your initial proportion estimate. For example, if you are conducting a survey among students trying to find out how many of them read more than 5 books last year, you may**know a result of a previous survey**— 40%. If you have no such estimate, use the conservative value of 50%.`n₁`

— Required sample size.

If your population is finite — for example, you are conducting a survey among students of only one faculty — you need to include a **correction** in the following form:

`n₂ = n₁ / (1 + n₁ / N)`

where:

`N`

— Total population size.`n₂`

— Size of the sample taken from the whole population that will make your research statistically significant.

## How to calculate sample size: an example

We will analyze a survey case step-by-step, so you can get a clear picture of **how to use our sample size calculator**. You are planning to conduct a survey to find out what is the proportion of students on your campus who regularly eat their lunch at the campus canteen.

- Decide
**how accurate**you want your result to be. Let's say that it is important for the canteen to know the result, with a margin of error of**2%**maximum. - Decide on your
**confidence level**. We can assume you want to be**99%**sure that your result is correct. - Do you have an
**initial proportion guess**? Let's say you accessed a similar survey from 10 years ago and the proportion was equal to**30%**. You can assume it as your initial estimate. - Is the
**total population**of students so high that you can assume it's**infinite**? Probably not. You need to find the current data for the number of students on the campus — let's assume it is**25,000**. - All you need to do now is to
**input all this data**into our sample size calculator. It finds the sample size required for the result to be statistically significant is**3,051**. You need to ask that many students the same question… Are you sure you can't settle for a 95% confidence level? 😀