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Sample Size Calculator

Find the sample size needed for a survey or calculate margin of error from confidence level, proportion, and population size.

Find Out the Sample Size

ExampleSample values — edit any field to see your result.

Use 50% when the expected proportion is unknown.

Leave blank for a large or unknown population.

Results update as you type.

Sample Size

385

Estimated result

Method
Cochran normal-approximation formula
Sample Size385

Use Sample size mode to plan a survey, or switch to Margin of error mode to evaluate an existing sample. Both modes support calculator.net's confidence levels, an expected proportion, and an optional finite population size.

Formula

For a large population, the required sample size is:

n = Z² × p(1 − p) / e²

where e is the margin of error as a decimal. For a finite population N:

n adjusted = n / (1 + (n − 1) / N)

Margin-of-error mode reverses the calculation:

e = Z × √(p(1 − p) / n)

Examples

Default sample-size calculation

At 95% confidence, 5% margin of error, and p = 50%, the unrounded result is about 384.15, so the required sample size is 385.

Known sample of 100

At 95% confidence with n = 100 and p = 60%, the margin of error is 9.60%.

Frequently asked questions

How large should my survey sample be?
It depends on the confidence level, desired margin of error, expected population proportion, and whether the total population is finite. At 95% confidence, 5% error, and 50% proportion, the large-population result is 385.
Why use 50% for an unknown population proportion?
A proportion of 50% maximizes p times one minus p, producing the most conservative and therefore largest required sample size.
What does population size change?
For a finite population, sampling without replacement reduces uncertainty. The finite population correction can therefore lower the required sample size or margin of error.
Why is the required size rounded up?
A fraction of a respondent cannot be sampled, and rounding down would fail to meet the target margin of error.

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