Sample Size Calculator

Proportion mode is for surveys where responses fall into categories, such as "yes/no", "agree/disagree", or multiple-choice questions. You specify the expected proportion (the estimated percentage that will answer one way) and the acceptable margin of error as a percentage. Mean mode is for measuring a continuous variable, such as average age, income, or test score. You specify the expected standard deviation of the population and the acceptable margin of error as an absolute value.

95% is the standard for most academic research and surveys, giving you 95% confidence that the true population value falls within your margin of error. 99% is used when the cost of error is very high, such as in medical research or policy decisions. 90% is acceptable for preliminary research, internal studies, or when collecting a larger sample is impractical. For most business surveys, 95% with a 5% margin of error is the conventional minimum standard.

When your population is small and finite, the standard sample size formula overestimates the required sample because it assumes an infinite population. The finite population correction formula adjusts for this: n = n₀ / (1 + (n₀ − 1) / N). For example, if the uncorrected estimate is 385 people but your total population is only 1,000, the FPC reduces the required sample to about 278. Leave the population field empty to assume an infinite (very large) population.

A proportion of 50% (p = 0.5) maximizes the variance term p × (1−p) = 0.25, producing the largest — and most conservative — sample size estimate. If you use 50% when you do not know the true proportion, you are guaranteed to have an adequate sample regardless of the actual result. If you have prior research suggesting the proportion is closer to 20% or 80%, entering that value will reduce the required sample size, potentially saving significant survey costs.

For national opinion polls, a margin of error of ±3% or ±5% at 95% confidence is standard. A ±5% margin of error at 95% confidence for an infinite population requires 385 respondents — the benchmark figure cited in most survey research guides. For internal quality checks or small business surveys, ±10% at 90% confidence may be acceptable. For medical or regulatory research, margins of ±1% or less at 99% confidence are often required, driving sample sizes into the thousands.

Switch to "평균 검정 (Mean Test)" mode and enter the standard deviation of the population you are studying. If you do not know the population standard deviation, you can estimate it from a pilot study or prior research, or use a conservative estimate equal to the range of expected values divided by 4 (the range rule of thumb). Then enter the margin of error as an absolute value — for example, if you want to estimate an average income within ±$500, enter 500 as the margin.

The sample size in this calculator is calculated for a given margin of error and confidence level, which corresponds to controlling the Type I error rate (false positive). Statistical power (1 − Type II error rate, the probability of detecting a true effect) is a separate consideration that also depends on sample size, but requires specifying an effect size. For power analysis, you need a dedicated power calculation tool. The sample sizes produced here are minimum sizes for estimation accuracy, not for hypothesis testing power.

Larger samples reduce sampling error, but with diminishing returns. Doubling the sample size reduces the margin of error by only a factor of √2 (about 1.41). Beyond the minimum required sample size, the additional precision gained from collecting more data must be weighed against the cost of data collection. Random sampling errors can also be dwarfed by systematic biases such as non-response bias or poorly worded survey questions, which no amount of additional sample size can fix.