Calculate the minimum sample size needed to achieve your target precision — for estimating means, detecting differences between two groups, or measuring proportions. Includes a precision vs sample size trade-off chart.
Select the study type, then fill in the inputs. All calculations use two-sided tests.
Choose your study type, enter the parameters, and press Calculate to see the minimum sample size with a precision trade-off chart.
The confidence level (e.g. 95%) is the probability that your interval contains the true value if you repeated the study many times. The margin of error is half the width of that interval. A wider margin means a less precise estimate but a smaller sample. Tighter precision always costs more samples.
Statistical power is the probability of correctly detecting a real difference between two groups. Low power means you risk missing real improvements — a false negative (Type II error). Most studies target 80–90% power. Higher power requires larger samples, especially when the difference you want to detect is small.
Halving the margin of error requires quadrupling the sample size (the relationship is quadratic, not linear). This is why the trade-off chart is curved. Beyond a certain point, collecting more data yields very little additional precision — and the chart shows exactly where that inflection point occurs for your specific inputs.