How Many People You Actually Need
The required sample for estimating a proportion is:
n = z² × p(1 − p) / e²
where z is the critical value for the confidence level, p is the expected proportion and e is the margin of error. At 95% confidence, ±3% and an unknown proportion, that gives 1,067 — which is why national polls cluster around a thousand respondents.
Sample Size Chart
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±1% | 6,765 | 9,604 | 16,587 |
| ±2% | 1,692 | 2,401 | 4,147 |
| ±3% | 752 | 1,068 | 1,843 |
| ±5% | 271 | 385 | 664 |
| ±10% | 68 | 97 | 166 |
Assuming a 50% expected proportion and a very large population. Halving the margin of error quadruples the sample, because e is squared in the denominator.
Population Size Barely Matters
The most counterintuitive result in survey statistics: polling a city of 100,000 and a country of 300 million to the same precision requires almost the same sample. The finite population correction only bites when the sample is a large fraction of the population — above roughly 5%.
| Population | Sample for ±5% at 95% |
|---|---|
| 500 | 218 |
| 1,000 | 278 |
| 10,000 | 370 |
| 100,000 | 383 |
| 10,000,000 | 385 |
Why 50% Is the Default
The term p(1−p) is maximised at p = 0.5, so assuming 50% gives the largest — and therefore safest — required sample. If prior work suggests the answer is near 10% or 90%, the required sample drops by nearly two-thirds.
The Response Rate Problem
These figures are completed responses, not invitations. At a 30% response rate, needing 385 completions means inviting about 1,300 people. Worse, low response rates introduce non-response bias — those who answer differ systematically from those who do not — and no sample size fixes that.
Frequently Asked Questions
Is a bigger sample always better?
Statistically yes, practically no. Beyond a point, extra respondents buy very little precision at substantial cost, and sampling quality matters far more than sampling quantity. A biased sample of 10,000 is worse than a representative sample of 500.
What about comparing subgroups?
Each subgroup needs its own adequate sample. A poll of 1,000 that reports on a subgroup of 80 respondents carries a margin of error above ±11% for that subgroup.
Does this apply to A/B testing?
Partly. A/B tests are about detecting a difference rather than estimating a value, so sample size there is driven by statistical power and the smallest effect worth detecting.