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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.

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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

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Sample Size385

Use Sample size mode to plan a survey, or switch to Margin of error mode to evaluate an existing sample. Choose a confidence level, expected proportion, and optional finite population size for either calculation.

How to use this calculator

In Sample size, enter a confidence level, margin of error, and expected population proportion. A margin of 5% means 5 percentage points: a 50% estimate has endpoints around 45% and 55%, not 47.5% and 52.5%. Use 50% for an unknown proportion because it gives the largest planning sample.

Leave Population size blank for a large or unknown population, or enter its size for the finite-population correction. The result is rounded up and counts completed responses, not invitations. If you need 385 completed responses and expect a 50% response rate, plan about 385 / 0.5 = 770 invitations, while accounting separately for selection and nonresponse bias.

In Margin of error, enter the completed sample size instead of a target margin. An entered finite population must be at least as large as the sample.

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.

A finite population of 1,000

With the same 95% confidence, 5-percentage-point margin, and 50% proportion, enter N = 1,000. The corrected size is about 277.73, so the tool rounds up to 278 completed responses. This correction assumes sampling without replacement from that population.

Known sample of 100

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

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)

For a finite population, margin-of-error mode also multiplies e by √((N − n) / (N − 1)). The displayed margin is in percentage points.

Planning assumptions

The result is a simple random-sample planning value based on the entered confidence level, margin of error, variability or proportion, and optional finite population. Clustering, design effects, stratification, nonresponse, unequal weights, subgroup targets, and model-based analyses can require a larger sample. Round the calculated requirement upward and document every assumption.

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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