Surveys Calculator
Survey Sample Size Calculator works out Recommended sample size and Unrounded requirement from Confidence level, Statistical power and Test sidedness. The default figures on this page give recommended sample size of 385; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- alpha = 1 - 95/100 = 0.05, two-sided, so z(alpha) = 1.959963985.
- z(beta) for 80% power = 0.841621234.
- n = z^2 p(1-p) / e^2 = 3.841458821 x 0.25 / 0.0025 = 384.145882
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
9 sources
What the Survey Sample Size Calculator calculates
Computes the sample size needed for a survey proportion, a mean, a comparison of two proportions or two means, a paired study, a correlation, a noninferiority or equivalence trial, a log-rank survival study, a diagnostic-accuracy study or a cluster-randomised trial, and works backwards to the margin of error or the power of a sample you already have.
How to use this Survey Sample Size Calculator
Enter Confidence level, Statistical power, Test sidedness and Expected proportion (group 1). Recommended sample size updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Recommended sample size, Unrounded requirement and Per group (group 1).
The method follows Cochran, W.G. (1977), Sampling Techniques, 3rd edition, Wiley, chapters 4 and 5, Raosoft Inc., Sample Size Calculator - stated formula, Fleiss, J.L., Levin, B. & Paik, M.C. (2003), Statistical Methods for Rates and Proportions, 3rd edition, Wiley, chapter 4, Chow, S.-C., Shao, J. & Wang, H. (2008), Sample Size Calculations in Clinical Research, 2nd edition, Chapman & Hall and Schoenfeld, D.A. (1983), "Sample-size formula for the proportional-hazards regression model", Biometrics 39(2), 499-503.
What you can compare
Change one input at a time to see how it affects Recommended sample size, Unrounded requirement and Per group (group 1). The inputs you can vary are Confidence level, Statistical power, Test sidedness, Expected proportion (group 1), Expected proportion (group 2) and Margin of error.
Understanding Recommended sample size, Unrounded requirement and Per group (group 1)
Sample-size calculations for clinical, regulatory or published research should be confirmed by a qualified statistician against the actual analysis plan before a study is registered or a protocol is finalised.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to calculate sample size for a survey?
Computes the sample size needed for a survey proportion, a mean, a comparison of two proportions or two means, a paired study, a correlation, a noninferiority or equivalence trial, a log-rank survival study. Open “How this is worked out” beside the result to see each step for your own figures.
Is 20 respondents enough for a survey?
Computes the sample size needed for a survey proportion, a mean, a comparison of two proportions or two means, a paired study, a correlation, a noninferiority or equivalence trial, a log-rank survival study. On the figures this page opens with — confidence level 95%, expected proportion (group 1) 50% and margin of error 5% — the recommended sample size is 385. Put your own figures in their place and the working updates beside the result.
What is a good sample size in a survey?
Computes the sample size needed for a survey proportion, a mean, a comparison of two proportions or two means, a paired study, a correlation, a noninferiority or equivalence trial, a log-rank survival study. On this page it is computed from Confidence level, Statistical power and Test sidedness and shown as Recommended sample size, Unrounded requirement and Per group (group 1).
What is a good sample size for a population of 50,000?
It needs Confidence level, Statistical power, Test sidedness, Expected proportion (group 1), Expected proportion (group 2) and Margin of error. Nothing else is required, and the figures stay in your browser.
What information do I need for the Survey Sample Size Calculator?
You need Confidence level, Statistical power, Test sidedness, Expected proportion (group 1), Expected proportion (group 2), Margin of error, Standard deviation and Margin of error (mean scale). The page opens with default figures that give recommended sample size of 385, so you can see the scale before entering your own.
What does this Survey Sample Size Calculator show?
It shows Recommended sample size, Unrounded requirement, Per group (group 1), Per group (group 2), Total across all groups, Recruit this many to allow for attrition, Required number of events and Design effect (DEFF), with the working and any warnings for your entries.