Enter your population size, confidence level, and margin of error to calculate the required sample size for your survey or study. The Sample Size Calculator also shows you the margin of error for any existing sample, so you can validate whether your data meets statistical standards.
Required Sample Size
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Actual Margin of Error
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Z-Score Used
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Sample as % of Population
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Sample size is the number of individuals selected from a population to participate in a survey or study. A properly calculated sample size ensures your results are statistically representative of the broader population, without needing to survey everyone.
A good sample size is one that achieves your desired confidence level and margin of error. For most surveys, a margin of error of ±5% with a 95% confidence level is considered the industry standard. Larger populations typically require larger samples, but the returns diminish quickly — a sample of ~385 is sufficient for nearly any population at 95% confidence and ±5% margin of error.
There's no universal definition, but samples over 1,000 are generally considered large in survey research. Large samples reduce the margin of error and increase statistical power, but they also increase cost and time. Beyond a certain point, increasing sample size yields diminishing improvements in accuracy.
The formula uses your confidence level (converted to a Z-score), margin of error, and estimated response distribution (p). For an infinite population: n = Z² × p × (1−p) / e². For a finite population, a correction factor is applied: n_adjusted = n / (1 + (n−1)/N), where N is the population size.
A Z-score represents the number of standard deviations from the mean corresponding to your chosen confidence level. For a 95% confidence level, the Z-score is 1.96; for 99% it is 2.576. A higher Z-score reflects greater certainty but requires a larger sample size.
Margin of error is the maximum expected difference between your sample results and the true population value. A smaller margin of error (e.g. ±1%) requires a much larger sample than a wider margin (e.g. ±5%). Halving the margin of error roughly quadruples the required sample size.
Response distribution (also called population proportion) is the estimated percentage of respondents who will select a particular answer. If you don't know this value, use 50% — it produces the largest (most conservative) sample size estimate and ensures your sample is sufficient regardless of actual responses.
Common mistakes include using too wide a margin of error (which makes results unreliable), assuming a small sample is fine for a large population, ignoring non-response rates (always collect more than the minimum), and forgetting to apply the finite population correction when your population is small.