Sample Size Calculator
Choose a confidence level, margin of error, and estimated proportion to find the minimum sample size needed.
How sample size is calculated
The formula n = (Z² × p × (1−p)) / E² estimates the minimum number of respondents needed for a survey, where Z is the z-score for your chosen confidence level, p is the estimated proportion of the population with the trait you're studying, and E is your acceptable margin of error.
When you don't know the true proportion in advance, using 50% is the conservative choice — it maximizes the required sample size, since p × (1−p) is largest at p = 0.5, so your actual needed sample will be the same or smaller than this estimate for any other true proportion.
Frequently asked questions
What confidence level should I use?
95% is the most common standard for surveys and research, balancing reliability against practical sample size. 99% requires a larger sample for tighter certainty; 90% needs a smaller sample but with less certainty.
Why does the estimated proportion matter if I don't know the answer yet?
It affects how much the sample size needs to shrink the margin of error. If you have no prior estimate, 50% is the safe default since it produces the largest (most conservative) required sample size.
Does this account for the total population size?
No — this uses the standard infinite-population formula, which is accurate when your population is large relative to the sample. For small, well-defined populations (like a company's 200 employees), a finite population correction would reduce the required sample size further.