Sample size calculator

How many responses you need.

Sample size needed

385

For a large or unknown population

Formula
n = z² × p(1 − p) ÷ e²
z for this confidence level
1.96
Without the population correction
385

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How to find the sample size you need

  1. Choose the confidence level, usually 95%, and the margin of error you can accept, such as 5%.
  2. Leave the expected proportion at 50% unless you have an earlier estimate: 50% gives the safest, largest sample.
  3. Enter the population size if it is small (a school, a company); leave it empty for a large population.

Margin of error and sample size

At 95% confidence and p = 50%:

Margin of error Sample size
10% 97
5% 385
3% 1,068
2% 2,401
1% 9,604

Halving the margin of error needs four times the sample. That is why most polls settle around 1,000 responses for about ±3%.

What it doesn’t cover

The formula assumes a random sample. A large but biased sample, such as only the people who chose to answer an online poll, can still be badly wrong.