Sample size calculator
How many people to survey for a given margin of error and confidence level.
About this calculator
This sample size calculator works out how many people you need to survey for results you can trust. Choose the confidence level and the margin of error you can accept.
Add the population size for a small group, such as a company's staff, to see the smaller sample it needs.
How it works
n = z² × p × (1 − p) ÷ e², where z comes from the confidence level, p is the expected proportion and e the margin of error. For a small population, n is reduced to n ÷ (1 + (n − 1) ÷ population).
Last reviewed:
Worked example
- Confidence level: 95%
- Margin of error: 5%
- Expected proportion: 50%
Sample size needed: 385
Common questions
How many survey responses do I need?
For a large population, about 385 for a 95% confidence level and a 5% margin of error. Halving the margin of error needs about four times as many.
What is a margin of error?
How far the survey result might be from the true value. A result of 60% with a 5% margin means the true figure is probably between 55% and 65%.
Does a bigger population need a bigger sample?
Only up to a point. Beyond a few thousand people, the sample size barely changes, which is why national polls can use around 1,000 people.
The story behind it
Where the idea came from: In 1936 a huge magazine poll of over two million people wrongly predicted that Alf Landon would beat Franklin Roosevelt, while George Gallup got it right with a much smaller, better-chosen sample.
The Literary Digest's sample came from phone books and car registrations, which at the time leaned towards wealthier voters. Gallup showed that a well-chosen sample beats a big one, and survey science was born.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
Meet the founder