Formula
n₀ = z² × p(1 − p) ÷ E²n = n₀ ÷ (1 + (n₀ − 1) ÷ N) (finite population) How it works
Before running a survey or poll, you need to know how many people to ask. The answer depends on three things: how confident you want to be (usually 95%), how precise you need the result to be (the margin of error, often ±5 percentage points), and how varied the answers are likely to be.
Variability is captured by p(1 − p), where p is the proportion you expect to answer “yes”. This product is largest when p = 50%, so if you have no prior estimate, 50% gives a sample big enough for any outcome. At 95% confidence and ±5%, that famous worst case needs 385 responses.
If the population is small — say, the 1,000 employees of one company — you can apply the finite population correction, which reduces the required sample because each response covers a meaningful share of everyone. For populations in the hundreds of thousands or more, the correction makes almost no difference.
Frequently asked questions
Why does a national poll only need about 1,000 people?
Precision depends mainly on the sample size, not the population size. About 1,000 random respondents give a margin of error near ±3% at 95% confidence, whether the country has 5 million or 300 million people.
Does this account for people who don’t respond?
No. This is the number of completed responses you need. If you expect a 20% response rate, invite five times as many people.
How do I halve the margin of error?
You need roughly four times the sample size, because the margin of error shrinks with the square root of n.