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Sample size calculator (surveys & prevalence)

How many respondents do you need? Choose your confidence level and margin of error — and, for small populations, apply the finite population correction. Includes a copy-ready methods sentence.

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Your numbers

How far the sample estimate may plausibly be from the true value (±).

Leave at 50% if unsure — that is the most conservative choice.

Only matters for small populations (e.g. one organization). Blank = effectively infinite.

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When to use this

Use this before fielding a survey, poll, or prevalence study whose key result is a proportion — the share of students who report burnout, the fraction of samples testing positive, the percentage of customers who would switch. It answers the budgeting question every proposal and ethics application asks: how many respondents are enough for the precision you claim? If your key outcome is a difference between two groups rather than a single proportion, use the two-group sample size calculator instead.

Key assumptions

  • Simple random sampling (or something close to it) — quota and convenience samples have no valid margin of error.
  • The outcome is a proportion; 50% is the worst case and therefore the safe default.
  • The finite population correction only matters when the sample would exceed roughly 5% of the population.

Common mistakes

  • Forgetting non-response: n is completed questionnaires, not invitations sent.
  • Reporting the margin of error of a convenience sample as if it were probability-based.
  • Using this for group comparisons — detecting a difference needs a power analysis, not a precision calculation.

Frequently asked questions

Why is 385 such a common answer?
With a 95% confidence level, a ±5% margin of error and the conservative 50% proportion, the formula gives n = 384.16, which rounds up to 385 — independent of population size once the population is large. That is why so many published surveys target ~400 respondents.
When does population size matter?
Only when it is small relative to the sample. Surveying a university department of 200 people, the finite population correction cuts the required n substantially (385 → 132). For a national population it changes nothing — 385 is enough whether the country has 1 million or 100 million people.
What margin of error should I choose?
±5% at 95% confidence is the convention for descriptive surveys. Tighten to ±3% when subgroup estimates matter (each subgroup effectively becomes its own survey), and remember that halving the margin of error roughly quadruples the required sample.

Related free tools

Sample size for two groupsEffect size (Cohen's d)Confidence intervalDescriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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