Sample Size Calculator

How this works

The calculator finds the number of completed responses needed to estimate a proportion (for example, the share of respondents who say "yes") within a chosen margin of error at a chosen confidence level. It assumes the most conservative case, a 50/50 split, which requires the largest sample, so the answer is safe whatever your real split turns out to be.

The formula

For an unknown or very large population, the sample size isn₀ = z² × p × (1 − p) ÷ e², where z is 1.645, 1.96 or 2.576 for 90%, 95% or 99% confidence, p is the assumed proportion (0.5 here), and e is the margin of error as a decimal.

If you enter a population size N, the finite population correction is applied:n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Results are rounded up to the next whole response.

If you choose an expected response rate, people to invite is the sample size divided by that rate, rounded up.

A worked example

At 95% confidence and a 5% margin of error, n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16, so you need 385 responses. If your population is 1,000 people, the correction brings that down to 278. At a 30% response rate, 385 responses means inviting about 1,284 people.

What this does not cover

Subgroups. The margin of error applies to the whole sample. A subgroup of 100 people within it has a wider margin.
Random sampling. The formula describes sampling error for a random sample. A convenience sample, such as whoever clicks a link, has no true margin of error.
Non-response bias. Reaching the target number does not remove bias if the people who answered differ from those who did not.
Clustered or stratified designs. These need a larger sample than the simple-random figure; multiply by the design effect.
Comparing groups. Detecting a difference between two groups needs a power calculation, not this one.

Source

The formula and the finite population correction are standard; see Cochran, W. G. (1977),Sampling Techniques, 3rd ed., Wiley.