The Sample Size Calculator finds how many people you need to survey for a given confidence level and margin of error, and the margin of error for an existing sample.
Sample size: 385
| Sample size needed | 385 |
| Z-score for confidence level | 1.9600 |
| Unrounded | 384.15 |
Margin of error: ±9.60%
| Margin of error | ±9.60% |
| Interval | 50.40% – 69.60% |
Surveys and experiments study a sample because measuring a whole population is usually impossible. Too small a sample gives unreliable results; too large wastes money. The right size depends on how confident you want to be, how much error you can accept and how varied the population is.
n₀ = z² × p(1 − p) ÷ e², where z is the z-score for the confidence level (1.96 for 95%), p the expected proportion and e the margin of error. For a finite population N, n = n₀ ÷ (1 + (n₀ − 1)/N).
Worked example (defaults): 95% confidence, ±5% margin and p = 50% give n₀ = 1.96² × 0.25 ÷ 0.0025 = 384.16, so survey 385 people.
Use 50% for the proportion if you do not know it; it gives the largest, safest sample. A 95% confidence level is standard. Halving the margin of error roughly quadruples the sample size.
A large sample does not fix bias. Random selection, good question wording and high response rates matter just as much. Online opt-in polls can be large but unrepresentative.
Does population size matter much? Only for small populations; above about 100,000 the sample barely changes.
What is a confidence level? How often intervals built this way would contain the true value.
Why 385 for most polls? It is the classic 95% ± 5% answer.