Sample Size Calculator
Find how many people you need to survey (or measure) to hit a chosen margin of error, with an optional correction for small populations.
How sample size is calculated
The formula turns the confidence interval around: instead of asking how wide the interval is for a given n, it asks what n makes the interval as narrow as you want. Because precision grows with √n, halving the margin of error needs four times as many responses, which is why national polls rarely go below ±3%.
A big sample doesn’t fix a biased one. The 1936 Literary Digest poll collected over two million ballots and still called the US presidential election wrong, because its mailing lists over-represented wealthier voters.
Frequently asked questions
Why is 385 the magic number for surveys?
At 95% confidence, a ±5% margin of error and the most cautious assumption p = 50%, the formula gives 1.96² × 0.25 ÷ 0.05² = 384.16, rounded up to 385. That holds for any large population, whether it is a city or a country.
Does population size matter?
Surprisingly little once the population is more than about 20 times the sample. The finite population correction only makes a real difference for small groups, like surveying a school of 600 students. Leave population blank for large or unknown populations.
What if I don’t know the expected proportion?
Use 50%. It gives the largest required sample, so your margin of error will be at most what you asked for whatever the true value turns out to be.
Is this the number of people to contact?
No, it is the number of completed responses. If you expect a 20% response rate, divide by 0.2 and contact five times as many people.
Can I use this for an experiment comparing two groups?
This page sizes a single estimate to a given precision. Comparing two groups to detect a difference needs a power calculation, which also depends on the effect size and desired power (usually 80%). The formula here is a lower bound, not a substitute.