Use the calculator below to find the ideal sample (N) from the desired margin of error, or to discover the margin of error of a sample you've already collected. The calculations use finite-population correction and the conservative assumption of maximum variability.
Find out how many responses you need to collect.
Required N by margin of error (confidence 95%)
Already collected? See how precise your result is.
The ideal sample is the number of responses you need to collect so that your research results properly represent the total universe of people you want to understand. The margin of error indicates how much the result obtained in the sample may vary from the population's real value. A 5% margin, for example, means a 60% result may actually fall between 55% and 65%.
Calculating the right sample size balances two goals: ensuring precision and reliability in the results and respecting the study's cost-benefit. Too small a sample yields fragile conclusions; too large a sample wastes time and budget with no relevant precision gain. The calculation helps find the optimal point.
We work with proportion and finite-population correction, assuming p = q = 0.5 (maximum variability):
N = (N · z² · p · q) / ((N − 1) · e² + z² · p · q) e = z · √(p·q / n) · √((N − n) / (N − 1))
z values by confidence level: 85% = 1.44 · 90% = 1.645 · 95% = 1.96 (default) · 99% = 2.576.
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