# Sample Size Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

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:

$n_1 = Z^2\cdot p \cdot \frac{1-p}{\mathrm{ME}^2}$

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.
• $\mathrm{ME}$ — Margin of error, also known as the confidence interval. It tells you that you can be sure (with a 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. You can learn more about it at our margin of error calculator.
• $p$ — 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%.
• $n_1$ — 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:

$n_2 = \frac{n_1}{1+\frac{n_1}{N}}$

where:

• $N$ — Total population size.
• $n_2$ — 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.

1. 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.

2. Decide on your confidence level. We can assume you want to be $99\%$ sure that your result is correct.

3. 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.

4. 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 $25,000$.

5. 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? 😀

## Other useful tools beyond the sample size calculator

Now that you know how to calculate sample size, you can go beyond and use it to calculate other statistics of interest in your research:

Bogna Szyk
Confidence level
%
Margin of error
%
Proportion estimate
%
Sample size
Correction for finite population
Population
Sample size
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