Enter your population size, confidence level, and margin of error to calculate the minimum sample size needed for statistically valid research. You can also use the Find Margin of Error section to work backwards from a known sample size. Perfect for surveys, studies, and experiments. Also try the Impact Factor Calculator.
Required Sample Size
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Margin of Error
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Confidence Interval (Lower)
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Confidence Interval (Upper)
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Population Sampled
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A sample size is the number of individuals or observations selected from a larger population to participate in a study. Researchers use samples because it is often impractical to study every member of a population. The goal is to choose a sample large enough to accurately represent the population.
A 95% confidence level is the most widely used standard in research and surveys. It means you can be 95% confident that your sample results reflect the true population values. For higher-stakes decisions, such as medical studies, a 99% confidence level may be more appropriate, though it requires a larger sample size.
A margin of error of ±5% is the most common choice for general surveys and research. A smaller margin of error (e.g. ±2%) yields more precise results but requires a significantly larger sample size. The right margin of error depends on how much uncertainty is acceptable given your study's purpose.
Response distribution (or population proportion) is your best estimate of the percentage of the population that has the characteristic you're studying. When this value is 50%, the variability in the population is maximized, which requires the largest possible sample size to detect. If you have prior data suggesting a different proportion, you can enter that value to potentially reduce the required sample size.
Surprisingly, population size has a relatively small impact on the required sample size, especially for large populations. For populations over 10,000, the required sample size changes very little. This is why national polls of millions of people can still be conducted with samples of just 1,000–2,000 respondents.
Sample size is the number of participants you need in your study, while margin of error describes how much your sample results may differ from the true population value. They are inversely related — a larger sample size produces a smaller margin of error, giving you more precise and reliable results.
If you already know your sample size and want to find the resulting margin of error, you can rearrange the sample size formula. Enter your known sample size, population size, confidence level, and response distribution, and solve for the margin of error. The formula is: Margin of Error = Z × sqrt(p(1−p)/n) adjusted for finite population correction when applicable.
If your population size is unknown or extremely large (e.g. all internet users), you can treat the population as infinite. In this case, enter a very large number (such as 10,000,000). For large populations, the finite population correction has negligible effect, and the required sample size converges to the formula without a population correction factor.