Sample Size Calculator
Find out how many people you need to survey. Pick a confidence level and margin of error, optionally add your population size, and get the required sample size with Cochran's formula worked through step by step.
Results
385
Required sample size
1.96
Z-score used
Infinite
Population
How this was calculated
n₀ = z²p(1−p) / e² = 1.96² × 0.5 × (1 − 0.5) / 0.05² = 0.9604 / 0.0025 = 384.16
Rounding up to a whole respondent gives a required sample size of 385. This assumes simple random sampling; add extra respondents to cover expected non-response.
Sample size at common margins of error (95% confidence)
| Margin of error | Required sample size |
|---|---|
| ±3% | 1068 |
| ±5% | 385 |
| ±10% | 97 |
Frequently Asked Questions
- How is the sample size calculated?
- The calculator uses Cochran's formula: n₀ = z²p(1−p)/e², where z is the z-score for your confidence level, p is the expected proportion, and e is the margin of error. If you enter a population size, the finite population correction n = n₀ / (1 + (n₀ − 1)/N) is applied. The result is always rounded up to a whole person.
- What confidence level should I choose?
- 95% is the standard choice in most academic and market research — it corresponds to a z-score of 1.96. Use 99% (z = 2.576) when the stakes of being wrong are high, or 90% (z = 1.645) for quick exploratory surveys where a smaller sample is acceptable.
- Why is the expected proportion set to 50% by default?
- The term p(1−p) in the formula is largest when p = 0.5, so 50% gives the most conservative (largest) sample size. If you have no prior estimate of the proportion, leaving it at 50% guarantees your sample is big enough whatever the true value turns out to be.
- What if I do not know my population size?
- Leave the population field blank and the calculator treats the population as effectively infinite, which is fine for large populations. The finite population correction only matters when the population is small relative to the sample — for populations above roughly 100,000 it makes almost no difference.
- Does a bigger population always need a bigger sample?
- No — this is a common misconception. Required sample size levels off as the population grows: surveying a country of 300 million needs barely more respondents than surveying a city of 100,000 at the same confidence level and margin of error.