The formula
How it works
Find how many people you need to survey to reach a chosen confidence level and margin of error. Enter your requirements and, optionally, the size of the population you are sampling from.
FAQ
Why does a smaller margin need a much bigger sample?
The margin of error appears squared in the formula, so halving it roughly quadruples the sample size. Tighter precision gets expensive fast, which is why most surveys settle around a 3–5% margin.
What proportion should I assume?
If you have no idea, use 50%. That gives the largest — and therefore safest — sample size, because the variation p(1−p) is greatest at one half.
Why does a higher confidence level increase the sample size?
A higher confidence level uses a larger z-score, which widens the range you are trying to guarantee, so more responses are needed to hold that wider guarantee with the same precision.
What happens if my population is small?
Enter the actual population size and the finite population correction will scale the sample down, since you cannot need more responses than there are people to survey.
Does this account for people who won’t respond?
No, it gives the number of completed responses you need. If you expect only part of the people you contact to reply, divide the result by your expected response rate to know how many to contact.
Is this the same as the sample size for an A/B test?
Not quite — A/B tests compare two groups and usually need a separate calculation that accounts for the difference you want to detect between them, rather than a single population estimate.
How is margin of error different from confidence level?
The confidence level is how sure you want to be that the true value falls within your result, while the margin of error is how wide that range is allowed to be — together they define how precise and how trustworthy your estimate is.
About the sample size calculator
This calculator works out how many people you need to survey for your results to be reliable. Sample size is the crucial decision in any poll or study: too small and the findings are just noise, too large and you waste time and money. By balancing the confidence level you want, the margin of error you can accept and the size of your population, it gives the smallest sample that still meets your standards.
How to use it
Choose your confidence level — 95% is standard — and the margin of error you can tolerate, such as ±5%. Leave the response proportion at 50% unless you have a good estimate, and enter your population size (or 0 if it is very large). The calculator returns the number of responses you need. For example, a 95% confidence level with a 5% margin needs about 385 responses from a large population.
The formula
The basic sample size is , where is the z-score for your confidence level (1.96 for 95%), is the expected proportion and is the margin of error as a decimal. For a limited population of size , this is scaled down with the finite population correction, , which matters when your sample is a big fraction of the whole group.
Where it is used
Pollsters, market researchers and scientists use it to plan surveys and experiments so their conclusions hold up. Businesses use it before running customer studies, and quality teams use it to decide how many items to inspect. Getting the sample size right is what lets a poll of a thousand people speak for a nation — and knowing the maths stops you being misled by a survey that was simply too small.