Calculate your sample size

Enter the population size and choose the confidence level and the margin of error. The result updates instantly.

Population size

Total number of people in the group you want to study. If you don't know it, leave it blank.

Confidence level (%)

How sure you want to be that the sample reflects the population. 95% is the most common.

Margin of error (%)

How much the sample result may differ from the population. 5% is typical.

Sample size

383

About this calculation

Sample size by precision

What is it?

It estimates how many people you need so that a percentage or mean obtained in your sample resembles that of the whole population, within a margin of error you choose and with a given confidence level.

When to use it

In surveys and descriptive studies, when your aim is to describe a population (for example, what percentage holds an opinion) rather than to test a hypothesis. To compare groups or relate variables, use the power calculator.

Example

You want to know student satisfaction at a university with 8,500 enrolled students, with 95% confidence and a ±5% margin of error.

This is how you would fill in the calculator:

Population size: 8500
Confidence level (%): 95
Margin of error (%): 5

Result: You need 368 participants.

If you don't know how many people make up your population, leave that field blank: the calculator assumes a large population.

How is it calculated?

It uses the formula for estimating a proportion under simple random sampling:

n₀ = Z² · p · (1 − p) / e²

Where Z depends on the confidence level (1.96 for 95%), e is the margin of error as a decimal and p is the expected proportion. It uses p = 0.5, the most conservative option, which gives the largest possible sample.

When you enter the population size (N), the finite population correction is applied:

n = n₀ / (1 + (n₀ − 1) / N)

The result is rounded up. If you expect some people not to respond, increase the sample by that proportion.

How to cite this tool

AtheneaLab. (2026). Calculate your sample size [Web application]. https://athenealab.com/en/sample-size/precision/

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