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Sample Size Calculator

Choose the confidence level, the margin of error and the expected proportion.

Confidence level
%
%

Use 50% if you do not know. It gives the largest sample size.

Optional. Reduces the sample size when your whole group is small.

This result is an estimate only. Double-check important figures before relying on them.

How it is calculated

  • n₀ = z² × p × (1 − p) ÷ e²
  • With a population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
  • z = 1.645, 1.96 or 2.576 for 90%, 95% and 99%

For the interval from a sample, use the confidence interval calculator.

Worked example

95% confidence, ±5% margin, p = 50%:

  • n₀ = 1.96² × 0.25 ÷ 0.0025 = 385
  • For a population of 1,000 you need 278

Why your number may differ

Low response rates mean you should invite more people than the sample size. The formula assumes random sampling.

Frequently asked questions

How is the sample size calculated?

n = z² × p × (1 − p) ÷ e², where z is the confidence value, p the expected proportion and e the margin of error. A correction is applied for a finite population.

Why use 50% for the proportion?

It gives the biggest sample size, so it is the safe choice when you have no idea what the answer will be.

Does the population matter?

Only for small groups. For a very large population, 385 responses give ±5% at 95% confidence, whether the group is 10,000 or 10 million.

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