Required Sample Size: The minimum number of responses (or observations) needed to estimate a proportion within your specified margin of error at the chosen confidence level. Collecting fewer responses widens the margin; collecting more narrows it.
Confidence Level: The probability that the true population value falls within the margin of error around your sample estimate. A 95% level means that if you repeated the survey many times, about 95 out of 100 intervals would contain the true proportion.
Margin of Error: The maximum expected difference between the sample proportion and the true population proportion. A ±5% margin means your result could be up to 5 percentage points above or below the real value.
How This Calculator Works
You choose a confidence level (which maps to a z-score), enter a margin of error and an expected population proportion. The formula n = z² × p(1−p) / e² gives the sample size for an infinitely large population. If you provide a finite population size, a correction factor reduces n because sampling a large share of a small population gives extra precision. The result is always rounded up to the next whole number.
Quick Questions
What proportion should I use if I have no idea?
Use 50%. A 50/50 split maximizes the variance term p(1−p), which gives the largest (most conservative) sample size. If the true proportion turns out to be farther from 50%, your margin of error will actually be smaller than planned.
When does the finite-population correction matter?
It makes a meaningful difference when your sample will cover more than about 5% of the total population. For very large populations (e.g., a national survey), leaving the population field empty is fine — the correction is negligible.
Does this work for means as well as proportions?
This formula is specifically for estimating a proportion (yes/no outcome). For a continuous variable like average income, you'd need a different formula that includes the population standard deviation.
Should I add extra to account for non-response?
Yes. This calculator gives the number of completed responses you need. If you expect a 40% response rate, divide the sample size by 0.40 to find how many invitations to send.