Find how many responses a survey needs for a chosen confidence level and margin of error, with an optional finite population correction.
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With confidence level 95%, margin of error (± %) 5, expected proportion (%) 50, population size 0, the required sample size is 385.
| Confidence level | 95% |
|---|---|
| Margin of error (± %) | 5 |
| Expected proportion (%) | 50 |
| Population size | 0 |
| Required sample size | 385 |
|---|---|
| Sample size before rounding up | 384.1458821 |
| Without a population correction | 384.1458821 |
| Z-score for the confidence level | 1.959963985 |
Choose how confident you want to be and how close the result should be to the true value. The expected proportion is your best guess at the answer you are measuring; 50% is the safe default because it gives the largest sample. If you are surveying a small, known group, enter its size to apply the finite population correction, which lowers the number needed.
n₀ = z² × p(1 − p) ÷ e². With a population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Round up to a whole response. Choose how confident you want to be and how close the result should be to the true value. The expected proportion is your best guess at the answer you are measuring; 50% is the safe default because it gives the largest sample. If you are surveying a small, known group, enter its size to apply the finite population correction, which lowers the number needed.
With confidence level 95%, margin of error (± %) 5, expected proportion (%) 50, population size 0, the required sample size is 385. Sample size before rounding up: 384.1458821; Without a population correction: 384.1458821; Z-score for the confidence level: 1.959963985.
This is an estimate based on the inputs and assumptions shown on this page, not professional advice. Check anything with financial, health or safety consequences independently.
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For a large population and an expected proportion of 50%, 385 responses. The unrounded figure is about 384.15, and the sample size is always rounded up.
For large populations the required sample barely changes: about 385 responses for a city or a country alike. The correction only matters when the sample would be a noticeable share of the whole group.
p(1 − p) is largest at 50%, so it gives the biggest required sample. If you are fairly sure the answer is near 10% or 90%, fewer responses are needed.