Sample Size Calculator
How many people do you need to survey? Get the sample size for any confidence level, margin of error and population – with a table to compare options.
The formula
For a proportion – the share of people who answer “yes” – the sample size is
n = z² × p(1 − p) / E²
- z – the critical value for your confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%
- p – the expected proportion; 50% gives the largest, safest sample when you have no idea
- E – the margin of error, as a decimal (5% = 0.05)
Worked example
95% confidence and a ±5% margin: n = 1.96² × 0.5 × 0.5 / 0.05² = 384.2, rounded up to 385 responses. That is why so many surveys aim for about 400 people.
Small populations
If you survey a group of known size – the employees of a company, the members of a club – enter the population size. The finite population correction n = n₀ / (1 + (n₀ − 1) / N) lowers the number: for 2,000 people you need 323 instead of 385. For populations above about 100,000 the correction hardly changes anything.
What matters most
Halving the margin of error roughly quadruples the sample: ±2.5% needs 1,537 responses at 95%. A national poll with ±3% needs 1,068. More important than the exact number is that the sample is random – 2,000 self-selected online answers can be less reliable than 400 random ones.
Plan for non-response
The result is the number of completed responses. If you expect 25% of people to answer, invite four times as many.
Frequently asked questions
How many responses do I need for a 95% confidence level?
385 for a ±5% margin of error, 1,068 for ±3% and 2,401 for ±2% (with p = 50%, large population).
Why use 50% as the expected proportion?
p(1 − p) is largest at 50%, so the sample is big enough whatever the true answer turns out to be.
Does the population size matter?
Only for small populations. For a city or a country the required sample is practically the same.