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Sample Size Calculator

Find how many responses you need for statistically reliable survey results.

How it is calculated

The tool uses Cochran's formula for estimating a proportion: n₀ = z² × p × (1 − p) / e², where z is the normal-distribution value for the confidence level, p the expected proportion (as a fraction) and e the margin of error (as a fraction). The supported confidence levels are 80, 85, 90, 95 and 99%, using z = 1.282, 1.440, 1.645, 1.960 and 2.576; any other level shows no result. If you give a population size above zero, a finite-population correction is applied: n = n₀ / (1 + (n₀ − 1) / N); without one, the adjusted and unadjusted figures are equal. Both results are rounded up to a whole person. Proportion defaults to 50%, the most cautious choice because it makes p(1 − p) largest, and must be between 0 and 100. Margin must be above zero.

Worked example

Confidence 95% (z = 1.96), margin of error 5%, proportion 50%, population 2000. Unadjusted size: n₀ = 1.96² × 0.5 × 0.5 / 0.05² = 0.9604 / 0.0025 = 384.16, rounded up to 385. Population correction: 384.16 / (1 + 383.16 / 2000) = 384.16 / 1.1916 = 322.4. Rounded up, you need 323 completed responses instead of 385, because a small population needs fewer answers for the same precision.

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Common mistakes

  • Counting people you contacted instead of people who answered. The result is the number of completed responses, so divide by your expected response rate to find how many invitations to send.
  • Typing the margin as 0.05. The field is a percentage, so ±5% is 5.
  • Choosing a proportion other than 50 without evidence. If you have no earlier estimate, leave it at 50, which gives the largest and safest sample. A proportion of 0 or 100 produces a size of 0, which is not a usable plan.
  • Entering a confidence level such as 97 and expecting an answer. Only 80, 85, 90, 95 and 99 are recognised; other levels show no result.
  • Giving a huge population and expecting a change. For large populations the correction is negligible, so the adjusted and unadjusted sizes are almost the same.

About this calculator

This calculator finds the survey sample size needed for statistically reliable results, using the standard formula built from your desired confidence level (like 95%), margin of error (like ±5%), and population size, based on the normal distribution's z-score.

Market researchers, academic survey designers, and UX researchers use it before launching a survey to know how many respondents to target — too few and the results aren't trustworthy, too many wastes time and budget collecting data you didn't need.

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Comments (1)

  • Editorial team

    The margin of error drives the answer far more than the population does. At 95% confidence and a 50% proportion, a 5-point margin asks for 385 completed responses, while a 3-point margin asks for 1,068. A small population changes things: with 500 in the group, the 5-point case drops to 218. Decide first what precision your decision needs. What response rate do you expect from your survey, and how many invitations will that mean?

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